Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
T\u1eadp h\u1ee3p \u2013 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p l\u00e0 b\u00e0i to\u00e1n gi\u00fap tr\u1ebb r\u00e8n luy\u1ec7n t\u01b0 duy. \u0110\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u1edf th\u00e0nh b\u00e0i h\u1ecdc \u0111\u1ea7u ti\u00ean trong ph\u1ea7n s\u1ed1 h\u1ecdc c\u1ee7a m\u00f4n to\u00e1n l\u1edbp 6. T\u1eadp h\u1ee3p \u2013 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng. Tr\u1ebb c\u1ea7n n\u1eafm v\u1eefng \u0111\u1ec3 ti\u1ebfp t\u1ee5c t\u01b0 duy logic v\u00e0 ph\u00e2n t\u00edch con s\u1ed1 \u1edf nh\u1eefng b\u00e0i ti\u1ebfp theo.<\/p>\n\n\n\n
\u0110\u1ecbnh ngh\u0129a t\u1eadp h\u1ee3p \u2013 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p<\/p>\n\n\n\n
Kh\u00e1i ni\u1ec7m v\u1ec1 t\u1eadp h\u1ee3p l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m n\u1ec1n t\u1ea3ng, c\u01a1 b\u1ea3n nh\u1ea5t c\u1ee7a to\u00e1n h\u1ecdc n\u00f3i chung v\u00e0 to\u00e1n l\u1edbp 6 n\u00f3i ri\u00eang. Nghi\u00ean c\u1ee9u ri\u00eang v\u1ec1 v\u1ea5n \u0111\u1ec1 n\u00e0y, to\u00e1n h\u1ecdc chia m\u1ed9t ng\u00e0nh ri\u00eang g\u1ecdi l\u00e0 \u201cL\u00fd thuy\u1ebft t\u1eadp h\u1ee3p\u201d.<\/p>\n\n\n\n
Nh\u00ecn chung, t\u1eadp h\u1ee3p l\u00e0 kh\u00e1i ni\u1ec7m kh\u00f4ng \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a. Tuy nhi\u00ean, c\u00f3 th\u1ec3 hi\u1ec3u T\u1eadp h\u1ee3p l\u00e0 s\u1ef1 bao h\u00e0m m\u1ed9t ho\u1eb7c nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng. C\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng trong t\u1eadp h\u1ee3p c\u00f3 nh\u1eefng \u0111i\u1ec3m chung v\u00e0 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 Ph\u1ea7n t\u1eed.<\/p>\n\n\n\n
V\u00ed d\u1ee5: T\u1eadp h\u1ee3p c\u00e1c lo\u1ea1i c\u00e2y h\u1ecd \u0111\u1eadu bao h\u00e0m c\u00e1c lo\u1ea1i c\u00e2y: C\u1ecf \u0111inh l\u0103ng, \u0111\u1eadu H\u00e0 Lan, \u0111\u1eadu Lupin, me, c\u00e2y g\u1ed7 th\u00f4ng v\u00e0ng,\u2026<\/p>\n\n\n\n
Trong v\u00ed d\u1ee5 n\u00e0y, c\u00e1c lo\u1ea1i c\u00e2y h\u1ecd \u0111\u1eadu l\u00e0 t\u1eadp h\u1ee3p.<\/p>\n\n\n\n
V\u00e0 c\u00e1c ph\u1ea7n t\u1eed bao g\u1ed3m: C\u1ecf \u0111inh l\u0103ng, \u0111\u1eadu H\u00e0 Lan,\u2026<\/p>\n\n\n\n
Xem th\u00eam : S\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a m\u1ed9t t\u1eadp h\u1ee3p. T\u1eadp h\u1ee3p con \u2013 B\u00e0i t\u1eadp to\u00e1n l\u1edbp 6<\/p><\/blockquote>\n\n\n\n
C\u00e1ch vi\u1ebft ph\u1ea7n t\u1eed \u2013 t\u1eadp h\u1ee3p c\u1ee7a ph\u1ea7n t\u1eed, quy t\u1eafc v\u00e0 c\u00e1c k\u00fd hi\u1ec7u li\u00ean quan<\/p>\n\n\n\n
C\u00e1ch vi\u1ebft t\u1eadp h\u1ee3p<\/p>\n\n\n\n
T\u00ean t\u1eadp h\u1ee3p \u0111\u01b0\u1ee3c vi\u1ebft \u0111\u1ea1i di\u1ec7n b\u1eb1ng c\u00e1c ch\u1eef c\u00e1i in hoa: A, B, C, D, \u2026<\/p>\n\n\n\n
C\u00f3 2 c\u00e1ch vi\u1ebft t\u1eadp h\u1ee3p:<\/p>\n\n\n\n
Li\u1ec7t k\u00ea c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p<\/p>\n\n\n\n
V\u00ed d\u1ee5: H = t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean nh\u1ecf h\u01a1n 10<\/p>\n\n\n\n
H = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 0}<\/p>\n\n\n\n
Ch\u1ec9 ra c\u00e1c t\u00ednh ch\u1ea5t \u0111\u1eb7c tr\u01b0ng c\u1ee7a t\u1eadp h\u1ee3p<\/p>\n\n\n\n
V\u00ed d\u1ee5: C = t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 12, nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng 200<\/p>\n\n\n\n
C = {x \u20ac \u2115\u250212< x \u2264 200}<\/p>\n\n\n\n
Ngo\u00e0i ra, th\u1ec3 hi\u1ec7n t\u1eadp h\u1ee3p c\u00f2n \u0111\u01b0\u1ee3c minh h\u1ecda b\u1eb1ng BI\u1ec2U \u0110\u1ed2 VEN<\/p>\n\n\n\n
Bi\u1ec3u \u0111\u1ed3 ven l\u00e0 m\u1ed9t v\u00f2ng tr\u00f2n k\u00edn ch\u1ee9a c\u00e1c ph\u1ea7n t\u1eed thu\u1ed9c t\u1eadp h\u1ee3p.<\/p>\n\n\n\n
V\u00ed d\u1ee5: A = t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 5 v\u00e0 nh\u1ecf h\u01a1n 11<\/p>\n\n\n\n
C\u00e1ch vi\u1ebft, quy t\u1eafc v\u00e0 c\u00e1c k\u00fd hi\u1ec7u li\u00ean quan<\/p>\n\n\n\n
C\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan \u0111\u1ebfn t\u1eadp h\u1ee3p<\/p>\n\n\n\n
T\u1eadp h\u1ee3p con<\/p>\n\n\n\n
N\u1ebfu c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p A \u0111\u1ec1u thu\u1ed9c t\u1eadp h\u1ee3p B v\u00e0 ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p B c\u00f3 ch\u1ee9a t\u1ea5t c\u1ea3 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p A. Ta n\u00f3i: A l\u00e0 t\u1eadp h\u1ee3p con c\u1ee7a B<\/p>\n\n\n\n
K\u00fd hi\u1ec7u: A \u2e26 B ho\u1eb7c B \u2e27 A<\/p>\n\n\n\n
T\u1eadp h\u1ee3p con<\/p>\n\n\n\n
Hai t\u1eadp h\u1ee3p b\u1eb1ng nhau<\/p>\n\n\n\n
Hai t\u1eadp h\u1ee3p b\u1eb1ng nhau \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 A = B. Ta n\u00f3i: t\u1eadp h\u1ee3p A b\u1eb1ng t\u1eadp h\u1ee3p B.<\/p>\n\n\n\n
Hai t\u1eadp h\u1ee3p b\u1eb1ng nhau khi m\u1ecdi ph\u1ea7n t\u1eed c\u1ee7a A \u0111\u1ec1u l\u00e0 ph\u1ea7n t\u1eed c\u1ee7a B v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. M\u1ecdi ph\u1ea7n t\u1eed c\u1ee7a B \u0111\u1ec1u l\u00e0 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p A<\/p>\n\n\n\n
Hai t\u1eadp h\u1ee3p b\u1eb1ng nhau<\/p>\n\n\n\n
Giao c\u1ee7a hai t\u1eadp h\u1ee3p<\/p>\n\n\n\n
Giao c\u1ee7a hai t\u1eadp h\u1ee3p l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p. M\u00e0 t\u1eadp h\u1ee3p \u0111\u00f3 ch\u1ee9a c\u00e1c ph\u1ea7n t\u1eed chung c\u1ee7a t\u1eadp h\u1ee3p A v\u00e0 t\u1eadp h\u1ee3p B.<\/p>\n\n\n\n
K\u00fd hi\u1ec7u: A \u2229 B<\/p>\n\n\n\n
Hai t\u1eadp h\u1ee3p b\u1eb1ng nhau<\/p>\n\n\n\n
M\u1ed9t s\u1ed1 k\u00fd hi\u1ec7u<\/p>\n\n\n\n
K\u00fd hi\u1ec7u t\u1eadp h\u1ee3p r\u1ed7ng: \u2205<\/p>\n\n\n\n
K\u00fd hi\u1ec7u m\u1ed9t ph\u1ea7n t\u1eed thu\u1ed9c t\u1eadp h\u1ee3p: \u2208<\/p>\n\n\n\n
K\u00fd hi\u1ec7u m\u1ed9t ph\u1ea7n t\u1eed kh\u00f4ng thu\u1ed9c t\u1eadp h\u1ee3p: \u2209<\/p>\n\n\n\n
T\u00ecm hi\u1ec3u th\u00eam : T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean. Vietlearn c\u00f9ng tr\u1ebb t\u00ecm hi\u1ec3u s\u1ed1 h\u1ecdc l\u1edbp 6<\/p><\/blockquote>\n\n\n\n
- \u0110\u00e1p \u00e1n b\u00e0i t\u1eadp s\u00e1ch gi\u00e1o khoa<\/li><\/ol>\n\n\n\n
B\u00e0i 1 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 1 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 2 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 2 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 3 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 3 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 4 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 4 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 5 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i 5 (Trang 6\/ sgk to\u00e1n 6 t\u1eadp 1)<\/p>\n\n\n\n
M\u1ed9t s\u1ed1 b\u00e0i t\u1eadp v\u00e0 l\u1eddi gi\u1ea3i b\u1ed5 sung<\/p>\n\n\n\n
B\u00e0i 1: \u201cCho hai t\u1eadp h\u1ee3p : A = {a, b} ; B = {b, x, y}. \u0110i\u1ec1n k\u00ed hi\u1ec7u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 ch\u1ea5m :<\/p>\n\n\n\n
x \u2026 A ; y \u2026 B ; b \u2026 A ; b \u2026 B.<\/p>\n\n\n\n
\u0110\u00e1p \u00e1n: x \u2208 A ; y \u2208 B ; b \u2208 A ; b \u2208 B.\u201d<\/p>\n\n\n\n
B\u00e0i 2: \u201cVi\u1ebft t\u1eadp h\u1ee3p M c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 m\u1ed9t ch\u1eef s\u1ed1 b\u1eb1ng 2 c\u00e1ch:<\/p>\n\n\n\n
\u0110\u00e1p \u00e1n: C\u00e1ch 1 : M = {0 ; 1; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9} .<\/p>\n\n\n\n
C\u00e1ch 2 : M = {x \u2208 N \/ x < 10} (N l\u00e0 k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean)<\/p>\n\n\n\n
Nh\u1eefng \u0111i\u1ec1u nh\u1ecf Vietlearn nh\u1eafn ba m\u1eb9<\/p>\n\n\n\n
\u0110\u1ec3 con chinh ph\u1ee5c \u0111\u01b0\u1ee3c ki\u1ebfn th\u1ee9c l\u1edbp 6<\/a> m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n, ba m\u1eb9 n\u00ean ch\u00fa \u00fd, quan t\u00e2m t\u1edbi s\u1ef1 thay \u0111\u1ed5i trong t\u00e2m l\u00fd v\u00e0 ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc c\u1ee7a con. Vi\u1ec7c d\u1ea1y con<\/a> h\u1ecdc \u0111\u1ec3 con t\u1ef1 tin h\u1ecdc l\u1edbp 6 n\u00ean \u0111\u01b0\u1ee3c ph\u1ee5 huynh ti\u1ebfn h\u00e0nh th\u01b0\u1eddng xuy\u00ean t\u1eeb nh\u1eefng \u0111i\u1ec1u nh\u1ecf nh\u1ea5t. Nh\u01b0 luy\u1ec7n ch\u1eef hay luy\u1ec7n l\u1ea1i c\u00e1c ph\u00e9p t\u00ednh nh\u1ea9m,\u2026 Ba m\u1eb9 n\u00ean nh\u1eafc nh\u1edf con h\u1ecdc v\u00e0 \u00f4n b\u00e0i cho k\u1ecbp ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc.<\/p>\n\n\n\n
Kho t\u00e0i li\u1ec7u h\u1ecdc t\u1eadp<\/a> Mi\u1ec5n Ph\u00ed \u2013 Vietlearn<\/p>\n\n\n\n
V\u00ec v\u1edbi kh\u1ed1i l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c l\u1edbn, n\u1ebfu con b\u1ecf b\u00ea d\u00f9 ch\u1ec9 1 ng\u00e0y, con r\u1ea5t c\u00f3 th\u1ec3 s\u1ebd b\u1ecb ch\u1eadm l\u1ea1i so v\u1edbi b\u1ea1n b\u00e8 c\u00f9ng l\u1edbp. C\u00f3 nh\u1eefng b\u00e0i t\u1eadp kh\u00f3, con s\u1ebd c\u1ea7n \u0111\u1ebfn s\u1ef1 gi\u1ea3i th\u00edch, gi\u00fap \u0111\u1ee1 c\u1ee7a ph\u1ee5 huynh. Trong kho\u1ea3ng th\u1eddi gian c\u00f9ng con h\u1ecdc t\u1eadp<\/a>, \u00f4n luy\u1ec7n, ba m\u1eb9 n\u00ean \u0111\u1ed9ng vi\u00ean con h\u0103ng h\u00e1i ph\u00e1t bi\u1ec3u \u00fd ki\u1ebfn \u1edf l\u1edbp. V\u00e0 m\u1ea1nh d\u1ea1n gi\u01a1 tay h\u1ecfi th\u00eam v\u1ec1 nh\u1eefng v\u1ea5n \u0111\u1ec1 con ch\u01b0a th\u1ef1c s\u1ef1 hi\u1ec3u r\u00f5. \u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c nguy\u00ean t\u1eafc khi d\u1ea1y con<\/a> h\u1ecdc l\u1edbp 6, Vietlearn g\u1eedi ba m\u1eb9 m\u1ed9t s\u1ed1 b\u00ed quy\u1ebft \u0111\u1ec3 con h\u1ecdc t\u1ed1t l\u1edbp 6<\/p>\n\n\n\n
L\u1eddi k\u1ebft:<\/p>\n\n\n\n
\u0110\u1ed1i v\u1edbi b\u00e0i h\u1ecdc \u0111\u1ea7u ti\u00ean trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n<\/a> h\u1ecdc l\u1edbp 6. Qua ph\u1ea7n tr\u00ecnh b\u00e0y l\u00fd thuy\u1ebft v\u00e0 g\u1ee3i \u00fd l\u1eddi gi\u1ea3i c\u1ee7a m\u00ecnh, Vietlearn mong r\u1eb1ng c\u00f3 th\u1ec3 h\u1ed7 tr\u1ee3 ba m\u1eb9 c\u0169ng nh\u01b0 c\u00e1c con trong qu\u00e1 tr\u00ecnh h\u1ecdc t\u1eadp<\/a> v\u00e0 r\u00e8n luy\u1ec7n t\u1ea1i tr\u01b0\u1eddng trung h\u1ecdc c\u01a1 s\u1edf. Ch\u00fac c\u00e1c con \u0111\u1ea1t \u0111\u01b0\u1ee3c nhi\u1ec1u th\u00e0nh t\u00edch v\u00e0 g\u1eb7t h\u00e1i \u0111\u01b0\u1ee3c nhi\u1ec1u ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 ph\u00e1t tri\u1ec3n th\u1eadt t\u1ed1t trong m\u1ed9t m\u00f4i tr\u01b0\u1eddng m\u1edbi. N\u1ebfu c\u00f3 \u00fd ki\u1ebfn nh<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn T\u1eadp h\u1ee3p \u2013 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p l\u00e0 b\u00e0i to\u00e1n gi\u00fap tr\u1ebb r\u00e8n luy\u1ec7n t\u01b0 duy. \u0110\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u1edf th\u00e0nh b\u00e0i h\u1ecdc \u0111\u1ea7u ti\u00ean trong ph\u1ea7n s\u1ed1 h\u1ecdc c\u1ee7a m\u00f4n to\u00e1n l\u1edbp 6. T\u1eadp h\u1ee3p \u2013 ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9,4],"tags":[],"class_list":["post-2589","post","type-post","status-publish","format-standard","hentry","category-toan-hoc","category-trung-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/2589","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=2589"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/2589\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=2589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=2589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=2589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}