{"id":300353,"date":"2023-12-27T21:21:50","date_gmt":"2023-12-27T14:21:50","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=300353"},"modified":"2023-12-27T21:21:50","modified_gmt":"2023-12-27T14:21:50","slug":"menh-de-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/menh-de-la-gi\/","title":{"rendered":"M\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec? M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 g\u00ec? C\u00e1c lo\u1ea1i m\u1ec7nh \u0111\u1ec1 c\u1ea7n ghi nh\u1edb"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">Trong l\u0129nh v\u1ef1c logic v\u00e0 to\u00e1n h\u1ecdc, c\u00f3 r\u1ea5t nhi\u1ec1u kh\u1ed1i l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n nh\u01b0ng l\u1ea1i \u0111\u00f3ng vai tr\u00f2 c\u1ef1c k\u1ef3 quan tr\u1ecdng. V\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u00ednh l\u00e0 m\u1ed9t trong s\u1ed1 \u0111\u00f3. Nh\u01b0ng \u0111i\u1ec1u g\u00ec t\u1ea1o n\u00ean m\u1ed9t m\u1ec7nh \u0111\u1ec1? <\/span><b>M\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\"> v\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn th\u00ec sao? Ch\u00ednh v\u00ec th\u1ebf, b\u00e0i vi\u1ebft sau \u0111\u00e2y c\u1ee7a <strong>Ho\u00e0ng H\u00e0 Mobile<\/strong> s\u1ebd gi\u00fap b\u1ea1n kh\u00e1m ph\u00e1 s\u00e2u h\u01a1n v\u1ec1 m\u1ec7nh \u0111\u1ec1 &#8211; t\u1eeb \u0111\u1ecbnh ngh\u0129a c\u01a1 b\u1ea3n \u0111\u1ebfn nh\u1eefng d\u1ea1ng ph\u1ee9c t\u1ea1p h\u01a1n, c\u00e1c lo\u1ea1i m\u1ec7nh \u0111\u1ec1 c\u1ea7n ghi nh\u1edb.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng, v\u00e0 trong ng\u1eef ph\u00e1p ti\u1ebfng Vi\u1ec7t, \u0111\u00f3 l\u00e0 m\u1ed9t c\u00e2u kh\u1eb3ng \u0111\u1ecbnh v\u1ec1 m\u1ed9t v\u1ea5n \u0111\u1ec1 n\u00e0o \u0111\u00f3. Nh\u01b0ng \u0111i\u1ec1u quan tr\u1ecdng m\u00e0 b\u1ea1n c\u1ea7n nh\u1edb l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 ch\u1ec9 c\u00f3 th\u1ec3 l\u00e0 \u0111\u00fang ho\u1eb7c sai, kh\u00f4ng th\u1ec3 v\u1eeba \u0111\u00fang v\u1eeba sai.<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-300354 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-1.jpg\" alt=\"menh-de-la-gi-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5, khi n\u00f3i &#8220;M\u1eb7t tr\u1eddi m\u1ecdc t\u1eeb ph\u00eda T\u00e2y&#8221;, c\u00e2u n\u00e0y l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai v\u00ec n\u00f3 kh\u00f4ng ph\u1ea3n \u00e1nh s\u1ef1 th\u1eadt. Trong khi \u0111\u00f3, c\u00e2u &#8220;Tr\u00e1i \u0111\u1ea5t quay quanh M\u1eb7t tr\u1eddi&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u00ec n\u00f3 di\u1ec5n \u0111\u1ea1t m\u1ed9t s\u1ef1 th\u1eadt c\u00f3 th\u1ec3 ki\u1ec3m ch\u1ee9ng \u0111\u01b0\u1ee3c.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00ean c\u1ea1nh \u0111\u00f3, ch\u1ec9 c\u00f3 c\u00e1c c\u00e2u mang t\u00ednh ch\u1ea5t kh\u1eb3ng \u0111\u1ecbnh m\u1edbi \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ec7nh \u0111\u1ec1. N\u00ean c\u00e2u c\u1ea3m th\u00e1n nh\u01b0 &#8220;Tr\u1eddi \u01a1i!&#8221;, hay nh\u1eefng c\u00e2u mang t\u00ednh ch\u1ea5t nghi v\u1ea5n nh\u01b0 &#8220;B\u1ea1n \u0111ang l\u00e0m g\u00ec?&#8221; s\u1ebd kh\u00f4ng c\u00f2n l\u00e0 m\u1ec7nh \u0111\u1ec1.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 g\u00ec?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 logic khi b\u1ea1n t\u00ecm hi\u1ec3u <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\">. \u0110\u00e2y l\u00e0 lo\u1ea1i m\u1ec7nh \u0111\u1ec1 m\u00e0 t\u00ednh \u0111\u00fang sai c\u1ee7a n\u00f3 ph\u1ee5 thu\u1ed9c v\u00e0o gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn trong m\u1ec7nh \u0111\u1ec1.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">\u00dd ngh\u0129a<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Nh\u1edd v\u00e0o t\u00ednh linh ho\u1ea1t c\u1ee7a m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn, ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng ch\u00fang trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau nh\u01b0 to\u00e1n h\u1ecdc, khoa h\u1ecdc m\u00e1y t\u00ednh, v\u00e0 logic \u0111\u1ec3 m\u00f4 t\u1ea3 c\u00e1c quy lu\u1eadt hay \u0111i\u1ec1u ki\u1ec7n c\u00f3 th\u1ec3 thay \u0111\u1ed5i t\u00f9y thu\u1ed9c v\u00e0o \u0111i\u1ec1u ki\u1ec7n \u0111\u1ea7u v\u00e0o kh\u00e1c nhau. \u0110i\u1ec1u n\u00e0y gi\u00fap ch\u00fang ta ph\u00e1t tri\u1ec3n c\u00e1c m\u00f4 h\u00ecnh v\u00e0 l\u00fd thuy\u1ebft c\u00f3 t\u00ednh linh ho\u1ea1t v\u00e0 \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c c\u1ee7a ki\u1ebfn th\u1ee9c.<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-300355 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-2.jpg\" alt=\"menh-de-la-gi-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda cho m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 c\u1ee5 th\u1ec3 v\u1ec1 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 khi ch\u00fang ta c\u00f3 m\u1ec7nh \u0111\u1ec1 P(n) v\u1edbi n l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, P(n) kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 c\u1ee5 th\u1ec3, m\u00e0 l\u00e0 m\u1ed9t m\u00f4 t\u1ea3 chung \u00e1p d\u1ee5ng cho m\u1ecdi s\u1ed1 nguy\u00ean t\u1ed1 n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Khi ch\u00fang ta th\u1eed nghi\u1ec7m v\u1edbi gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3, nh\u01b0 P(2), ch\u00fang ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1. N\u1ebfu P(2) l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang, t\u1ee9c l\u00e0 khi n = 2 th\u00ec m\u1ec7nh \u0111\u1ec1 P(n) l\u00e0 \u0111\u00fang. Tuy nhi\u00ean, khi th\u1eed v\u1edbi P(6), v\u1edbi n = 6 th\u00ec m\u1ec7nh \u0111\u1ec1 P(n) tr\u1edf th\u00e0nh m\u1ec7nh \u0111\u1ec1 sai.<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-300356 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-3.jpg\" alt=\"menh-de-la-gi-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">\u0110i\u1ec1u quan tr\u1ecdng trong m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 kh\u1ea3 n\u0103ng thay \u0111\u1ed5i gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn \u0111\u1ec3 ki\u1ec3m tra t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1. M\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn n s\u1ebd t\u1ea1o ra m\u1ed9t m\u1ec7nh \u0111\u1ec1 c\u1ee5 th\u1ec3 v\u00e0 sau \u0111\u00f3 b\u1ea1n m\u1edbi c\u00f3 th\u1ec3 \u0111\u00e1nh gi\u00e1 l\u00e0 \u0111\u00fang hay sai.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">C\u00e1c lo\u1ea1i m\u1ec7nh \u0111\u1ec1 c\u1ea7n ghi nh\u1edb<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Trong l\u0129nh v\u1ef1c logic v\u00e0 to\u00e1n h\u1ecdc, vi\u1ec7c bi\u1ebft <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\"> v\u00e0 hi\u1ec3u r\u00f5 v\u1ec1 c\u00e1c lo\u1ea1i m\u1ec7nh \u0111\u1ec1 l\u00e0 v\u00f4 c\u00f9ng quan tr\u1ecdng \u0111\u1ec3 \u00e1p d\u1ee5ng ch\u00fang v\u00e0o vi\u1ec7c suy lu\u1eadn v\u00e0 ch\u1ee9ng minh logic. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 nh\u1eefng lo\u1ea1i m\u1ec7nh \u0111\u1ec1 c\u1ea7n ghi nh\u1edb:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng, \u0111\u00e2y l\u00e0 c\u00e1ch di\u1ec5n \u0111\u1ea1t m\u1ed9t m\u1ec7nh \u0111\u1ec1 theo h\u01b0\u1edbng tr\u00e1i ng\u01b0\u1ee3c ho\u00e0n to\u00e0n v\u1edbi m\u1ec7nh \u0111\u1ec1 g\u1ed1c.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Khi ch\u00fang ta c\u00f3 m\u1ed9t m\u1ec7nh \u0111\u1ec1 P, m\u1ec7nh \u0111\u1ec1 &#8220;kh\u00f4ng ph\u1ea3i P&#8221; \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P, v\u00e0 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 \u00acP. \u0110\u1eb7c \u0111i\u1ec3m quan tr\u1ecdng c\u1ee7a m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh l\u00e0 n\u00f3 lu\u00f4n c\u00f3 t\u00ednh ch\u1ea5t ng\u01b0\u1ee3c \u0111\u1ea3o v\u1edbi m\u1ec7nh \u0111\u1ec1 g\u1ed1c: n\u1ebfu m\u1ec7nh \u0111\u1ec1 P ban \u0111\u1ea7u \u0111\u00fang th\u00ec m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a n\u00f3 \u00acP s\u1ebd l\u00e0 m\u1ec7nh \u0111\u1ec1 sai, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300357 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-4.jpg\" alt=\"menh-de-la-gi-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">B\u00ean c\u1ea1nh \u0111\u00f3, m\u1ed9t m\u1ec7nh \u0111\u1ec1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c di\u1ec5n \u0111\u1ea1t theo nhi\u1ec1u c\u00e1ch kh\u00e1c nhau \u0111\u1ec3 th\u1ec3 hi\u1ec7n t\u00ednh ph\u1ee7 \u0111\u1ecbnh. V\u00ed d\u1ee5, khi c\u00f3 m\u1ec7nh \u0111\u1ec1 P: &#8220;t\u1ed5ng 2 c\u1ea1nh c\u1ee7a tam gi\u00e1c l\u1edbn h\u01a1n c\u1ea1nh c\u00f2n l\u1ea1i&#8221;, ch\u00fang ta c\u00f3 th\u1ec3 di\u1ec5n \u0111\u1ea1t m\u1ec7nh \u0111\u1ec1 n\u00e0y theo h\u01b0\u1edbng ph\u1ee7 \u0111\u1ecbnh b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c c\u1ea5u tr\u00fac ng\u1eef ph\u00e1p kh\u00e1c nhau nh\u01b0 sau:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00acP c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c di\u1ec5n \u0111\u1ea1t d\u01b0\u1edbi d\u1ea1ng: &#8220;t\u1ed5ng 2 c\u1ea1nh c\u1ee7a tam gi\u00e1c nh\u1ecf h\u01a1n c\u1ea1nh c\u00f2n l\u1ea1i&#8221;<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Ho\u1eb7c: &#8220;t\u1ed5ng 2 c\u1ea1nh c\u1ee7a tam gi\u00e1c kh\u00f4ng l\u1edbn h\u01a1n c\u1ea1nh c\u00f2n l\u1ea1i&#8221;.\u00a0<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">C\u1ea3 hai c\u00e1ch di\u1ec5n \u0111\u1ea1t n\u00e0y \u0111\u1ec1u th\u1ec3 hi\u1ec7n m\u1ed9t g\u00f3c nh\u00ecn ph\u1ee7 \u0111\u1ecbnh v\u1ec1 m\u1ec7nh \u0111\u1ec1 g\u1ed1c P, \u00e1nh x\u1ea1 ra m\u1ed9t \u00fd ngh\u0129a kh\u00e1c ho\u00e0n to\u00e0n.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 k\u00e9o theo<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">M\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m kh\u00e1c \u201c<\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec\u201d<\/b><span style=\"font-weight: 400;\"> m\u00e0 b\u1ea1n c\u1ea7n nh\u1edb l\u00e0 m\u1ec7nh \u0111\u1ec1 k\u00e9o theo. N\u00f3 gi\u00fap x\u00e1c \u0111\u1ecbnh m\u1ed1i quan h\u1ec7 logic gi\u1eefa hai m\u1ec7nh \u0111\u1ec1 P v\u00e0 Q. Khi c\u00f3 hai m\u1ec7nh \u0111\u1ec1 P v\u00e0 Q, m\u1ec7nh \u0111\u1ec1 &#8220;N\u1ebfu P th\u00ec Q&#8221; \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 P\u21d2Q.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 k\u00e9o theo c\u00f3 t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t: n\u00f3 ch\u1ec9 sai khi m\u1ec7nh \u0111\u1ec1 P \u0111\u00fang m\u00e0 m\u1ec7nh \u0111\u1ec1 Q l\u1ea1i sai. N\u1ebfu P \u0111\u00fang v\u00e0 Q c\u0169ng \u0111\u00fang ho\u1eb7c n\u1ebfu P sai, th\u00ec m\u1ec7nh \u0111\u1ec1 k\u00e9o theo s\u1ebd \u0111\u01b0\u1ee3c coi l\u00e0 \u0111\u00fang.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300358 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-5.jpg\" alt=\"menh-de-la-gi-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5, gi\u1ea3 s\u1eed c\u00f3 m\u1ec7nh \u0111\u1ec1: &#8220;n\u1ebfu tam gi\u00e1c ABC c\u00f3 3 g\u00f3c b\u1eb1ng nhau th\u00ec tam gi\u00e1c ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u&#8221;. Trong \u0111\u00f3, m\u1ec7nh \u0111\u1ec1 P l\u00e0 &#8220;tam gi\u00e1c ABC c\u00f3 3 g\u00f3c b\u1eb1ng nhau&#8221;, v\u00e0 m\u1ec7nh \u0111\u1ec1 Q l\u00e0 &#8220;tam gi\u00e1c ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u&#8221;.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Khi \u00e1p d\u1ee5ng m\u1ec7nh \u0111\u1ec1 k\u00e9o theo v\u00e0o v\u00ed d\u1ee5 n\u00e0y, n\u1ebfu tam gi\u00e1c ABC c\u00f3 3 g\u00f3c b\u1eb1ng nhau (m\u1ec7nh \u0111\u1ec1 P \u0111\u00fang), v\u00e0 sau \u0111\u00f3 tam gi\u00e1c ABC c\u0169ng l\u00e0 tam gi\u00e1c \u0111\u1ec1u (m\u1ec7nh \u0111\u1ec1 Q \u0111\u00fang), th\u00ec m\u1ec7nh \u0111\u1ec1 k\u00e9o theo P\u21d2Q l\u00e0 \u0111\u00fang. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu tam gi\u00e1c ABC c\u00f3 3 g\u00f3c b\u1eb1ng nhau (P \u0111\u00fang), nh\u01b0ng l\u1ea1i kh\u00f4ng ph\u1ea3i l\u00e0 tam gi\u00e1c \u0111\u1ec1u (Q sai), th\u00ec m\u1ec7nh \u0111\u1ec1 k\u00e9o theo s\u1ebd tr\u1edf th\u00e0nh sai.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o \u2013 hai m\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o v\u00e0 m\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng l\u00e0 hai kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong logic, gi\u00fap ch\u00fang ta hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec <\/b><span style=\"font-weight: 400;\">v\u00e0 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c m\u1ec7nh \u0111\u1ec1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Khi ta c\u00f3 m\u1ed9t m\u1ec7nh \u0111\u1ec1 P\u21d2Q, m\u1ec7nh \u0111\u1ec1 Q\u21d2P \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o c\u1ee7a P\u21d2Q. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 n\u1ebfu P d\u1eabn \u0111\u1ebfn Q, th\u00ec Q c\u0169ng d\u1eabn \u0111\u1ebfn P. \u0110\u00e2y l\u00e0 m\u1ed9t quan h\u1ec7 hai chi\u1ec1u, m\u1ed7i m\u1ec7nh \u0111\u1ec1 d\u1eabn \u0111\u1ebfn m\u1ed9t m\u1ec7nh \u0111\u1ec1 kh\u00e1c v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300359 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-6.jpg\" alt=\"menh-de-la-gi-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 P \u21d4 Q \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng, khi v\u00e0 ch\u1ec9 khi m\u1ec7nh \u0111\u1ec1 P v\u00e0 m\u1ec7nh \u0111\u1ec1 Q c\u00f9ng \u0111\u00fang ho\u1eb7c c\u00f9ng sai. Khi P \u21d4 Q \u0111\u00fang, ngh\u0129a l\u00e0 c\u1ea3 hai m\u1ec7nh \u0111\u1ec1 P v\u00e0 Q c\u00f9ng \u0111\u00fang ho\u1eb7c c\u00f9ng sai, v\u00e0 khi P \u21d4 Q sai, ngh\u0129a l\u00e0 m\u1ed9t trong hai m\u1ec7nh \u0111\u1ec1 P ho\u1eb7c Q \u0111\u00fang, v\u00e0 m\u1ec7nh \u0111\u1ec1 c\u00f2n l\u1ea1i kh\u00e1c s\u1ebd sai.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5, gi\u1ea3 s\u1eed c\u00f3 m\u1ec7nh \u0111\u1ec1: &#8220;N\u1ebfu x l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean th\u00ec x + 5 c\u0169ng l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean&#8221; v\u00e0 &#8220;N\u1ebfu x + 5 l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean th\u00ec x c\u0169ng l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean&#8221;. Hai m\u1ec7nh \u0111\u1ec1 n\u00e0y t\u1ea1o th\u00e0nh m\u1ed9t c\u1eb7p m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o. N\u1ebfu x l\u00e0 s\u1ed1 nguy\u00ean, th\u00ec x + 5 c\u0169ng l\u00e0 s\u1ed1 nguy\u00ean v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. \u0110\u00e2y c\u0169ng l\u00e0 m\u1ed9t c\u1eb7p m\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u00ec c\u1ea3 hai \u0111\u1ec1u di\u1ec5n \u0111\u1ea1t c\u00f9ng m\u1ed9t \u00fd ngh\u0129a v\u1ec1 t\u00ednh nguy\u00ean c\u1ee7a x v\u00e0 x + 5.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 l\u01b0u \u00fd khi nh\u1eadn di\u1ec7n m\u1ec7nh \u0111\u1ec1<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Trong to\u00e1n h\u1ecdc, khi n\u00f3i v\u1ec1 <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\">, ch\u00fang ta c\u1ea7n ch\u00fa \u00fd \u0111\u1ebfn hai k\u00fd hi\u1ec7u quan tr\u1ecdng: \u2200 v\u00e0 \u2203, \u0111\u00f3 l\u00e0 v\u1edbi m\u1ecdi v\u00e0 t\u1ed3n t\u1ea1i.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">K\u00ed hi\u1ec7u \u2200, c\u00f2n g\u1ecdi l\u00e0 &#8220;v\u1edbi m\u1ecdi&#8221;, th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi di\u1ec5n \u0111\u1ea1t m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang cho t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn n\u00e0o \u0111\u00f3 thu\u1ed9c m\u1ed9t t\u1eadp h\u1ee3p X. V\u00ed d\u1ee5, khi c\u00f3 m\u1ed9t m\u1ec7nh \u0111\u1ec1 Q(n) v\u1edbi n thu\u1ed9c t\u1eadp X, c\u00e2u kh\u1eb3ng \u0111\u1ecbnh &#8220;V\u1edbi m\u1ecdi n b\u1ea5t k\u1ef3 thu\u1ed9c X, th\u00ec Q(n) \u0111\u00fang&#8221; \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng k\u00ed hi\u1ec7u \u2200n \u2208 X : Q(n).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">K\u00ed hi\u1ec7u \u2203, t\u1ee9c l\u00e0 &#8220;t\u1ed3n t\u1ea1i&#8221;, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi ta mu\u1ed1n di\u1ec5n \u0111\u1ea1t r\u1eb1ng t\u1ed3n t\u1ea1i \u00edt nh\u1ea5t m\u1ed9t gi\u00e1 tr\u1ecb n thu\u1ed9c t\u1eadp X \u0111\u1ec3 m\u1ec7nh \u0111\u1ec1 Q(n) l\u00e0 \u0111\u00fang. V\u00ed d\u1ee5, n\u1ebfu ta mu\u1ed1n n\u00f3i &#8220;C\u00f3 \u00edt nh\u1ea5t m\u1ed9t n thu\u1ed9c X sao cho Q(n) l\u00e0 \u0111\u00fang&#8221;, ch\u00fang ta s\u1eed d\u1ee5ng k\u00ed hi\u1ec7u \u2203n \u2208 X : Q(n).<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300360 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-7.jpg\" alt=\"menh-de-la-gi-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i ra, khi n\u00f3i v\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng gi\u1eefa hai m\u1ec7nh \u0111\u1ec1 P v\u00e0 Q, \u0111i\u1ec1u quan tr\u1ecdng c\u1ea7n nh\u1edb kh\u00f4ng ph\u1ea3i l\u00e0 n\u1ed9i dung c\u1ee7a ch\u00fang gi\u1ed1ng nhau ho\u00e0n to\u00e0n, m\u00e0 l\u00e0 ch\u00fang c\u00f9ng \u0111\u00fang ho\u1eb7c c\u00f9ng sai trong m\u1ecdi tr\u01b0\u1eddng h\u1ee3p. T\u01b0\u01a1ng \u0111\u01b0\u01a1ng ch\u1ec9 \u00e1m ch\u1ec9 r\u1eb1ng P v\u00e0 Q \u0111\u1ed3ng th\u1eddi \u0111\u00fang ho\u1eb7c \u0111\u1ed3ng th\u1eddi sai, kh\u00f4ng nh\u1ea5t thi\u1ebft ph\u1ea3i c\u00f3 c\u00f9ng \u00fd ngh\u0129a hay n\u1ed9i dung. Ch\u00fang ch\u1ec9 c\u00f3 th\u1ec3 n\u00f3i l\u00ean m\u1ed9t gi\u00e1 tr\u1ecb ch\u00e2n l\u00fd chung, kh\u00f4ng nh\u1ea5t thi\u1ebft ph\u1ea3i gi\u1ed1ng h\u1ec7t nhau.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Tham kh\u1ea3o m\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 m\u1ec7nh \u0111\u1ec1<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 nh\u1eefng kh\u00e1i ni\u1ec7m v\u1ec1 <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\"> \u1edf tr\u00ean, ch\u00fang ta s\u1ebd \u0111i s\u00e2u h\u01a1n v\u1ec1 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 ch\u00fang v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebfti.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng 1: X\u00e1c \u0111\u1ecbnh t\u00ednh \u0111\u00fang &#8211; sai<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 x\u00e1c \u0111\u1ecbnh t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ec7nh \u0111\u1ec1, ch\u00fang ta c\u1ea7n nh\u00ecn v\u00e0o \u0111\u1ecbnh ngh\u0129a c\u01a1 b\u1ea3n c\u1ee7a m\u1ec7nh \u0111\u1ec1 v\u00e0 \u00e1p d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p ph\u00f9 h\u1ee3p. M\u1ec7nh \u0111\u1ec1 l\u00e0 m\u1ed9t tuy\u00ean b\u1ed1 c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c t\u00ednh \u0111\u00fang sai c\u1ee7a n\u00f3.<\/span><\/p>\n<h4><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 1:\u00a0<\/span><\/h4>\n<p><span style=\"font-weight: 400;\">Cho ch\u00fang ta c\u00e1c c\u00e2u \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh li\u1ec7u ch\u00fang c\u00f3 ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1 hay kh\u00f4ng v\u00e0 t\u00ednh \u0111\u00fang sai c\u1ee7a t\u1eebng c\u00e2u:<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\">a) &#8220;Tr\u1eddi h\u00f4m nay \u0111\u1eb9p qu\u00e1!&#8221; kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1 v\u00ec n\u00f3 l\u00e0 m\u1ed9t c\u00e2u c\u1ea3m th\u00e1n, kh\u00f4ng c\u00f3 t\u00ednh \u0111\u00fang sai c\u1ee5 th\u1ec3.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">b) &#8220;Ph\u01b0\u01a1ng tr\u00ecnh x\u00b2 &#8211; 3x + 1 = 0 v\u00f4 nghi\u1ec7m&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai v\u00ec ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">c) &#8220;15 kh\u00f4ng l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u00ec 15 chia h\u1ebft cho 3 v\u00e0 5.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">e) &#8220;S\u1ed1 n c\u00f3 nh\u1ecf h\u01a1n 5 kh\u00f4ng?&#8221; kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1 v\u00ec n\u00f3 l\u00e0 m\u1ed9t c\u00e2u h\u1ecfi, kh\u00f4ng c\u00f3 tuy\u00ean b\u1ed1 c\u1ee5 th\u1ec3.<\/span><\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300361 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-8.jpg\" alt=\"menh-de-la-gi-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\">f) &#8220;Italia v\u00f4 \u0111\u1ecbch World Cup 2006&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang n\u1ebfu c\u00f3 d\u1eabn ch\u1ee9ng x\u00e1c th\u1ef1c v\u1ec1 s\u1ef1 ki\u1ec7n \u0111\u00f3.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">g) &#8220;Hai tam gi\u00e1c b\u1eb1ng nhau khi v\u00e0 ch\u1ec9 khi ch\u00fang c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai, v\u00ec hai tam gi\u00e1c c\u00f3 th\u1ec3 c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau m\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i b\u1eb1ng nhau.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">h) &#8220;M\u1ed9t t\u1ee9 gi\u00e1c l\u00e0 h\u00ecnh thoi khi v\u00e0 ch\u1ec9 khi n\u00f3 c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c v\u1edbi nhau&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<\/span><\/li>\n<\/ol>\n<h4><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 2:\u00a0<\/span><\/h4>\n<p><b>M\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec? <\/b><span style=\"font-weight: 400;\">X\u00e1c \u0111\u1ecbnh t\u00ednh \u0111\u00fang &#8211; sai c\u1ee7a c\u00e1c v\u00ed d\u1ee5 sau:<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\">a) &#8220;2 l\u00e0 s\u1ed1 ch\u1eb5n&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">b) &#8220;2 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1&#8221; c\u0169ng l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u00ec 2 ch\u1ec9 chia h\u1ebft cho 1 v\u00e0 ch\u00ednh n\u00f3.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">c) &#8220;2 l\u00e0 s\u1ed1 ch\u00ednh ph\u01b0\u01a1ng&#8221; l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai v\u00ec s\u1ed1 ch\u00ednh ph\u01b0\u01a1ng c\u00f3 ch\u1eef s\u1ed1 cu\u1ed1i l\u00e0 0, 1, 4, 5, 6, ho\u1eb7c 9, nh\u01b0ng 2 kh\u00f4ng th\u1ecfa \u0111i\u1ec1u ki\u1ec7n n\u00e0y.<\/span><\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300362 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-9.jpg\" alt=\"menh-de-la-gi-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng 2: X\u00e1c \u0111\u1ecbnh m\u1ed1i quan h\u1ec7 logic<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Trong to\u00e1n h\u1ecdc, c\u00e1c ph\u00e9p to\u00e1n v\u1ec1 m\u1ec7nh \u0111\u1ec1 nh\u01b0 k\u00e9o theo v\u00e0 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng gi\u00fap ch\u00fang ta x\u00e1c \u0111\u1ecbnh <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\"> v\u00e0 m\u1ed1i quan h\u1ec7 logic gi\u1eefa c\u00e1c tuy\u00ean b\u1ed1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 1: Cho m\u1ed9t ph\u00e1t bi\u1ec3u m\u1ec7nh \u0111\u1ec1 P \u21d2 Q v\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o c\u1ee7a n\u00f3, y\u00eau c\u1ea7u x\u00e1c \u0111\u1ecbnh t\u00ednh \u0111\u00fang sai c\u1ee7a ch\u00fang:<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\">a) P: &#8220;T\u1ee9 gi\u00e1c ABCD ch\u00ednh l\u00e0 h\u00ecnh thoi&#8221; v\u00e0 Q: &#8220;T\u1ee9 gi\u00e1c ABCD c\u00f3 c\u00e1ch c\u1ea1nh l\u00e0 AC v\u00e0 BD, ch\u00fang c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111o\u1ea1n.&#8221;<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 P \u21d2 Q: &#8220;N\u1ebfu t\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh thoi th\u00ec AC v\u00e0 BD c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.&#8221; \u0110\u00e2y l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o Q \u21d2 P: &#8220;N\u1ebfu t\u1ee9 gi\u00e1c ABCD c\u00f3 AC v\u00e0 BD c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng th\u00ec ABCD l\u00e0 h\u00ecnh thoi.&#8221; \u0110i\u1ec1u n\u00e0y l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai.<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300363 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-10.jpg\" alt=\"menh-de-la-gi-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 2: \u0111\u01b0a ra m\u1ed9t ph\u00e1t bi\u1ec3u P \u21d4 Q v\u00e0 y\u00eau c\u1ea7u \u0111\u00e1nh gi\u00e1 t\u00ednh \u0111\u00fang sai c\u1ee7a n\u00f3:<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\">a) P: &#8220;T\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh thoi&#8221; v\u00e0 Q: &#8220;T\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 2 \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c v\u1edbi nhau.&#8221;<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u1ec7nh \u0111\u1ec1 P \u21d4 Q: &#8220;T\u1ee9 gi\u00e1c ABCD s\u1ebd \u0111\u01b0\u1ee3c xem l\u00e0 h\u00ecnh thoi khi v\u00e0 ch\u1ec9 khi ABCD ch\u00ednh l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh v\u00e0 t\u1ee9 gi\u00e1c n\u00e0y s\u1edf h\u1eefu 2 \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c v\u1edbi nhau.&#8221; \u0110\u00e2y l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u00ec c\u1ea3 P \u21d2 Q v\u00e0 Q \u21d2 P \u0111\u1ec1u \u0111\u00fang, c\u00f3 ngh\u0129a l\u00e0 khi P th\u00ec Q, v\u00e0 khi Q th\u00ec P. M\u1ed1i quan h\u1ec7 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng gi\u1eefa hai m\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u01b0\u1ee3c x\u00e1c nh\u1eadn.<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng 3: Ch\u1ee9ng minh m\u1ec7nh \u0111\u1ec1<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 ch\u1ee9ng minh m\u1ed9t quy lu\u1eadt hay <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\">, ta th\u01b0\u1eddng s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh b\u1eb1ng ph\u1ea3n ch\u1ee9ng.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Trong v\u00ed d\u1ee5 n\u00e0y ch\u00fang ta c\u1ea7n ch\u1ee9ng minh r\u1eb1ng &#8220;n\u1ebfu n2 l\u00e0 s\u1ed1 ch\u1eb5n th\u00ec n c\u0169ng l\u00e0 s\u1ed1 ch\u1eb5n&#8221;<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300364 size-full\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-11.jpg\" alt=\"menh-de-la-gi-11\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-11.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-11-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/menh-de-la-gi-11-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">C\u00e1ch l\u00e0m:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ph\u1ea3n ch\u1ee9ng cho m\u1ec7nh \u0111\u1ec1 tr\u00ean: &#8220;n\u1ebfu n2 l\u00e0 s\u1ed1 ch\u1eb5n th\u00ec n s\u1ebd l\u00e0 s\u1ed1 l\u1ebb.&#8221;<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Do \u0111\u00f3: N\u1ebfu n l\u00e0 s\u1ed1 ch\u1eb5n th\u00ec khi \u0111\u00f3, n c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng n=2p v\u1edbi p l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean. Suy ra 2p+1 s\u1ebd cho ra con s\u1ed1 l\u1ebb<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Bi\u1ec3u th\u1ee9c ph\u1ea3n ch\u1ee9ng s\u1ebd l\u00e0 : n2=(2p+1)2 \u00a0 \u00a0 (1)<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Theo \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">n2=(2p+1)2 = 2(2p2 + 2p) + 1\u00a0 \u00a0 \u00a0 (2)<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u1eb7t: k=2p2 + 2p th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (2) s\u1ebd tr\u1edf th\u00e0nh<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">n2 = 2k + 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (3)<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh (3), ta s\u1ebd th\u1ea5y n2 s\u1ebd cho ra con s\u1ed1 l\u1ebb. \u0110i\u1ec1u n\u00e0y tr\u00e1i ng\u01b0\u1ee3c v\u00e0 khi\u1ebfn cho ph\u1ea3n ch\u1ee9ng m\u00e0 ch\u00fang ta \u0111\u01b0a ra ban \u0111\u1ea7u s\u1ebd sai. Cho n\u00ean, m\u1ec7nh \u0111\u1ec1 \u201cn\u1ebfu n2 l\u00e0 s\u1ed1 ch\u1eb5n th\u00ec n c\u0169ng l\u00e0 s\u1ed1 ch\u1eb5n\u201d \u0111\u00e3 \u0111\u00fang.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">C\u00f3 th\u1ec3 th\u1ea5y, ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh b\u1eb1ng ph\u1ea3n ch\u1ee9ng gi\u00fap ch\u00fang ta x\u00e1c nh\u1eadn t\u00ednh ch\u00ednh x\u00e1c c\u1ee7a m\u1ed9t quy lu\u1eadt hay m\u1ec7nh \u0111\u1ec1 b\u1eb1ng c\u00e1ch ch\u1ee9ng minh r\u1eb1ng vi\u1ec7c ph\u1ee7 \u0111\u1ecbnh gi\u1ea3 thi\u1ebft d\u1eabn \u0111\u1ebfn m\u00e2u thu\u1eabn v\u1edbi nh\u1eefng g\u00ec \u0111\u00e3 bi\u1ebft.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">L\u1eddi k\u1ebft<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Vi\u1ec7c hi\u1ec3u v\u1ec1 <\/span><b>m\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec<\/b><span style=\"font-weight: 400;\"> v\u00e0 c\u00e1c d\u1ea1ng kh\u00e1c nhau c\u1ee7a ch\u00fang gi\u00fap ch\u00fang ta x\u00e2y d\u1ef1ng n\u1ec1n t\u1ea3ng v\u1eefng ch\u1eafc trong logic v\u00e0 to\u00e1n h\u1ecdc. M\u1ed7i lo\u1ea1i m\u1ec7nh \u0111\u1ec1 \u0111\u1ec1u c\u00f3 t\u00ednh ch\u1ea5t v\u00e0 quy lu\u1eadt ri\u00eang, t\u1eeb \u0111\u01a1n gi\u1ea3n \u0111\u1ebfn m\u1ec7nh \u0111\u1ec1 ph\u1ee9c t\u1ea1p. \u0110\u1ed3ng th\u1eddi, vi\u1ec7c nh\u1eadn bi\u1ebft m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn v\u00e0 \u00e1p d\u1ee5ng c\u00e1c ph\u00e9p to\u00e1n logic nh\u01b0 k\u00e9o theo, t\u01b0\u01a1ng \u0111\u01b0\u01a1ng hay ph\u1ea3n ch\u1ee9ng gi\u00fap ch\u00fang ta ph\u00e1t tri\u1ec3n k\u1ef9 n\u0103ng suy lu\u1eadn v\u00e0 ch\u1ee9ng minh logic. Quan tr\u1ecdng nh\u1ea5t, ki\u1ebfn th\u1ee9c v\u1ec1 m\u1ec7nh \u0111\u1ec1 kh\u00f4ng ch\u1ec9 h\u1ed7 tr\u1ee3 trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc m\u00e0 c\u00f2n m\u1edf ra c\u01a1 h\u1ed9i \u00e1p d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c c\u1ee7a cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y c\u1ee7a ch\u00fang ta.<\/span><\/p>\n<p>XEM TH\u00caM:<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-cau\/\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/a><\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/truc-tam\/\">Tr\u1ef1c t\u00e2m l\u00e0 g\u00ec? X\u00e1c \u0111\u1ecbnh tr\u1ef1c t\u00e2m trong tam gi\u00e1c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trong l\u0129nh v\u1ef1c logic v\u00e0 to\u00e1n h\u1ecdc, c\u00f3 r\u1ea5t nhi\u1ec1u kh\u1ed1i l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n nh\u01b0ng l\u1ea1i \u0111\u00f3ng vai tr\u00f2 c\u1ef1c k\u1ef3 quan tr\u1ecdng. V\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u00ednh l\u00e0 m\u1ed9t trong s\u1ed1 \u0111\u00f3. Nh\u01b0ng \u0111i\u1ec1u g\u00ec t\u1ea1o n\u00ean m\u1ed9t m\u1ec7nh \u0111\u1ec1? M\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec v\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn th\u00ec sao? Ch\u00ednh v\u00ec [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":300365,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-300353","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>M\u1ec7nh \u0111\u1ec1 l\u00e0 g\u00ec? M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 g\u00ec? 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