Судоплатов С.В., Овчинникова Е.В. Дискретная математика
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ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
121 |
Вариант 3
1.A \ B = A [ B,
A £ (B n C) = (A £ B) n (A £ C).
2.n3 + 11n кратно 6 для всех n 2 !.
3.jAj > !, jBj < ! ) jA n Bj = jAj.
4.P1 = fha; 2i; ha; 3i; ha; 4i; hb; 3i; hc; 1i; hc; 4ig,
P2 = fh1; 1i; h2; 3i; h2; 2i; h3; 4i; h1; 4i; h2; 4i; h4; 2ig.
5.P µ (Z+)2, hx; yi 2 P , x2 > y, где Z+ = fx 2 Z j x > 0g.
6.hC n R; +; ¡; p ; 2 ¡ {:i.
7.B = hC; ¢i, X = f3{:g.
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10.xj(y © (y _ x)), x ! (y # (z $ xy)).
11.x # (yjz) и (x # y)j(x # z).
12.((x # y) ! (z $ y).
13.f(0; 1; 1) = f(1; 0; 0) = f(1; 0; 1) = 1.
14.(0001 0011 1100 1110).
15.J = fx © y; x _ yg.
16.(A [ B) © (A \ C) = A © (B n C).
122 |
ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
Вариант 4
1.A n (B [ C) = (A n B) \ (A n C), A £ (B \ C) = (A £ B) \ (A £ C).
2.1 ¢ 4 + 2 ¢ 7 + 3 ¢ 10 + ¢ ¢ ¢ + n(3n + 1) = n(n + 1)2.
3.! + ! = !.
4.P1 = fha; 1i; ha; 2i; hb; 3i; hc; 2i; hc; 3i; hc; 4ig,
P2 = fh1; 1i; h2; 1i; h2; 2i; h2; 3i; h2; 4i; h3; 3i; h4; 4ig.
5.P µ R2, hx; yi 2 P , x2 + y2 = 1.
6.hC n R; +; ¢; :i.
7.B = hC; +; {:i, X = R.
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10. x © (y ! (y $ x)), x # (yj(z _ xy)).
11. x $ (yjz) и (x $ y)j(x $ z).
12. ((x # y) ! z) $ y.
13. f(0; 0; 1) = f(1; 0; 0) = f(1; 1; 0) = 1.
14. (0011 1100 0011 0101).
15. J = fx ^ y; x ! yg.
16. (A [ B) n (B \ C) = (A n B) [ (A n C).
ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
123 |
Вариант 5
1.(A [ B) n C = (A n C) [ (B n C), (A \ B) £ C = (A £ C) \ (B £ C).
2.10n ¡ 1 кратно 9 для всех n 2 !.
3.[0; 1] [ [2; 3] » [0; 1].
4.P1 = fha; 1i; ha; 2i; ha; 3i; ha; 4i; hb; 3i; hc; 2ig,
P2 = fh1; 1i; h1; 4i; h2; 2i; h2; 3i; h3; 3i; h3; 2i; h4; 1i; h4; 4ig.
5.P µ R2, hx; yi 2 P , x ¢ y > 1.
6.h!; +; 0i.
7.B = hZ; +; ¡i, X = f¡5; 4g.
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10. |
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(x _ y) ! (y © x), x # (y $ (z # xy)). |
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11. |
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x ! (y $ z) и (x ! y) $ (x ! z). |
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! (z $ y). |
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f(0; 1; 1) = f(0; 1; 0) = f(1; 0; 0) = f(1; 0; 1) = 0. |
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14. |
(1010 0010 1101 0111). |
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15. |
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J = fx # y; x $ yg. |
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16. |
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(A n B) [ (C n B) = (B [ C) n A. |
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124 ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ
Вариант 6
1. A [ B = A \ B,
(A \ (B) £ (C \ D) = (A £ C) \ (B £ D).
2. 1 ¢ 2 + 2 ¢ 3 + 3 ¢ 4 + : : : + n(n + 1) = n(n+1)(n+2).
3
3.2! + 2! = 2!.
4.P1 = fha; 1i; ha; 2i; ha; 4i; hc; 3i; hc; 2i; hc; 4ig,
P2 = fh2; 1i; h3; 1i; h3; 2i; h4; 1i; h4; 3ig.
5.P µ R2, hx; yi 2 P , y = jxj.
6.hQ n Z; +; ¢; :i.
7.B = hZ; +; ¢i, X = f¡5g.
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10.x $ (y ^ (y ! x)), x _ (y © (z # xjy)).
11.x ! (y # z) и (x ! y) # (x ! z).
12.((x $ y) ! z)jy.
13.f(0; 1; 1) = f(0; 1; 0) = f(1; 0; 1) = f(1; 1; 1) = 1.
14.(0011 1101 0010 1100).
15.J = fx _ y; x $ yg.
16.A n (B n C) = (A n B) n C.²
ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
125 |
Вариант 7
1.A n (B \ C) = (A n B) [ (A n C),
(A n B) £ C = (A £ C) n (B £ C).
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3.[a; b] » R.
4.P1 = fha; 1i; ha; 2i; hb; 2i; hb; 4i; hc; 3i; hc; 2ig,
P2 = fh1; 1i; h1; 2i; h2; 2i; h3; 3i; h4; 3i; h4; 4ig.
5.P µ R2, hx; yi 2 P , x2 + x = y2 + y.
6.hR; ¢; :; ¡1i.
7.B = hZ; +; ¡i, X = f¡3; 4g.
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10. (x _ y) $ (y # x), xjy) ! (z © xy).
11. x ! (y © z) и (x ! y) © (x ! z).
12. (x _ y) ! (z © x).
13. f(0; 1; 0) = f(1; 0; 0) = f(1; 0; 1) = 0.
14. (1101 1101 0011 0011).
15. J = fx _ y; x © yg.
16. (A [ B) n (C \ A) = (B n C) n (A [ C).
126 |
ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
Вариант 8
1.A [ B = A \ B,
C µ D ) A £ C µ B £ D.
2.(1 ¡ 14)(1 ¡ 19)(1 ¡ 161 ) : : : (1 ¡ n12 ) = n2+1n для n > 2.
3.jZ £ Qj = !.
4.P1 = fha; 1i; ha; 4i; hb; 2i; hb; 3i; hc; 1i; hc; 4ig,
P2 = fh1; 1i; h1; 4i; h2; 1i; h3; 4i; h4; 3i; h4; 1ig.
5.P µ R2, hx; yi 2 P , x ¡ y 2 Z.
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10.(x $ y) _ (y # x), ((x ! y)jz) © xy.
11.xj(y ! z) и (xjy) ! (xjz).
12.(x _ y) ! (z © x).
13.f(0; 1; 1) = f(1; 0; 0) = f(1; 1; 0) = 0.
14.(1111 1100 1011 1011).
15.J = fx ! y; x ^ yg.
16.(A [ B) n (C \ B) = (A n C) [ (A n B).
ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
127 |
Вариант 9
1. (A \ B) n C = (A n C) \ (B n C),
(A £ B) [ (C £ D) µ (A [ C) £ (B [ D).
2. 12 + 22 + 32 + : : : + n2 = n(n+1)(2n+1). 6
3.[0; 1] » [0; 1).
4.P1 = fha; 1i; ha; 2i; ha; 4i; hb; 1i; hb; 4i; hc; 3ig,
P2 = fh1; 1i; h2; 4i; h2; 1i; h3; 3i; h4; 2i; h4; 1ig.
5.P µ R2, hx; yi 2 P , x + y = ¡2.
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x ^ (y © z) и (x ^ y) © (x ^ z). |
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f(0; 0; 0) = f(0; 0; 1) = f(1; 0; 1) = f(1; 1; 1) = 1. |
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(1110 0101 0011 0101). |
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J = fx $ y; xjyg. |
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(A [ C) n (B \ A) = (A n B) n (A \ C). |
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ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
Вариант 10
1.A [ (A \ B) = A \ (A [ B) = A,
(A [ B) £ (C [ D) = (A £ C) [ (B £ C) [ (A £ D) [ (B £ D).
2.2!1 + 3!2 + : : : + nn¡!1 = 1 ¡ n1! для n > 2.
3.[0; 1] » (0; 1].
4.P1 = fha; 1i; hb; 3i; hb; 1i; hb; 4i; hc; 3i; hc; 2ig,
P2 = fh1; 3i; h1; 4i; h2; 2i; h3; 3i; h4; 3i; h4; 4ig.
5.P µ R2, hx; yi 2 P , x2 + y2 = 4.
6.hZ; +; ¡; ¡2i.
7.B = hR n f0g; :; 1i, X = f2g.
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(x $ y) _ (y # x), ((x ! y)jz) © xy. |
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11. |
x ^ (y © z) и (x ^ y) © (x ^ z). |
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(x _ y) ! |
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f(0; 0; 1) = f(1; 1; 1) = f(1; 1; 0) = 0. |
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(1101 0011 1101 0011). |
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(A \ B) [ (A n C) = A n (B [ C). |
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ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
129 |
Вариант 11
1.(A n B) n C = A n (B [ C),
A µ C, B µ D ) A £ B = (A £ D) \ (C £ B).
2.1 ¢ 2 + 2 ¢ 5 + 3 ¢ 8 + : : : + n(3n ¡ 1) = n2(n + 1).
3.!2 » !3.
4.P1 = fha; 1i; hb; 3i; hc; 1i; hc; 4i; hc; 3i; hc; 2ig,
P2 = fh1; 1i; h1; 2i; h1; 4i; h2; 1i; h2; 2i; h2; 3i h3; 3i; h3; 2i, h3; 4i; h4; 3i; h4; 4i; h4; 1ig.
5.P µ R2, hx; yi 2 P , y < x ¡ 1.
6.P1 = fha; 2i; ha; 4i; hb; 3i; hc; 1i; hc; 2ig,
P2 = fh1; 1i; h1; 3i; h2; 4i; h3; 1i; h3; 4i; h4; 3i; h4; 2ig.
7.P µ Z2, hx; yi 2 P , x2 + y2 = 1.
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x ^ (y ! z) и (x ^ y) ! (x ^ z). |
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f(0; 0; 0) = f(1; 1; 1) = f(1; 1; 0) = 0. |
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(1100 1011 1111 1011). |
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J = fx ! y; x ^ yg. |
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(A n B) [ (A n C) = A n (B [ C). |
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130 |
ВАРИАНТЫ КОНТРОЛЬНОЙ РАБОТЫ |
Вариант 12
1.A n (B n C) = (A n B) [ (A \ C), U2 n (A £ B) = (A £ U) [ (U £ B).
2.n3 + 5n кратно 6 для всех n 2 !.
3.! + n = !.
4.P1 = fha; 1i; ha; 2i; ha; 4i; hb; 3i; hc; 1i; hc; 4ig,
P2 = fh1; 3i; h1; 2i; h2; 3i; h3; 2i; h3; 4i; h4; 1ig.
5.P µ R2, hx; yi 2 P , x2 = y.
6.hR n Z; +; ¢i.
7.B = hQ; ¢; 12i, X = f3g.
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10.(x © y) $ (yjx), ((x # y) $ z) _ xy.
11.x ^ (y $ z) и (x ^ y) $ (x ^ z).
12.(xjy) © (z ! x).
13.f(0; 0; 1) = f(0; 1; 1) = f(1; 1; 0) = f(1; 1; 1) = 1.
14.(0101 0101 1110 0011).
15.J = fx $ y; xjyg.
16.(A n B) \ (A n C) = A n (B \ C).©@©²¡¡ @@²²