《离散数学第二章解答》由会员分享，可在线阅读，更多相关《离散数学第二章解答（4页珍藏版）》请在金锄头文库上搜索。
1、部分I第二章习题解答习题习题 2.1:?题? (1). ? M(x) : x ?; L(x) : x?; ?题?x(M(x) L(x) (2). ? M(x) : x ?; C(x) : x?; ?题?x(M(x) C(x) (3). ? B(x) : x ?; F(x) : x?; ?题?x(B(x) F(x) (4). ? L(x,y,z) : x?y?z?; a :?;b :?;c :?; ?题?L(a,b,c) (5). ? P(x,y) : x?y; C(x,y) : x?y?; a :?;b :?; ?题? x(C(x,b) P(a,x) (6). ? O(x) : x?; E(x
2、) : x?; M(x) : x? ?题? x(M(x) O(x) E(x) (7). ? D(x) : x?;M(x,y) : x?y;P(x) : x?;a :?; ?题?D(a) x(P(y) M(a,x) (8). ? M(x) : x?; T(x) : x?;R(x,y) : x?y? ?题? x(M(x) yT(y) R(x,y)习题习题 2.2:?分?N ?R? ? (1). (x)(y)(x y = 1) ?x, ?y?x y = 1. ?N?R,?题? (2). (x)(y)(x y = x) ?x, ?y?x y = x. ?N?R,?题? (3). (x)(y)(x +
3、y = 0) ?x, ?y?x + y = 0. ?N?题?;?R?题? (4). (x)(y)(z)(x + y = z) ?x, ?y?z?x + y = z. ?N?R,?题?1习题习题 2.3:?D = a,b,c? (1). (x)P(x) (y)Q(y) (2). (x)P(x) (y)Q(y) (3). (y)P(y) (x)Q(x) (4). (x)(P(x) (y)Q(y) 解: (1). (x)P(x) (y)Q(y) (P(a) P(b) P(c) (Q(a) Q(b) Q(c) (2). (x)P(x) (y)Q(y) (P(a) P(b) P(c) (Q(a) Q(b
4、) Q(c) (3). (y)P(y) (x)Q(x) (P(a) P(b) P(c) (Q(a) Q(b) Q(c) (4). (x)(P(x) (y)Q(y) (x)P(x) (y)Q(y) (x)P(x) (y)Q(y) (P(a) P(b) P(c) (Q(a) Q(b) Q(c)习题习题 2.4:? (1). x(P(x,z) Q(y) (y)S(x,y) (2). (x)(P(x) Q(x) (R(x) (z)S(x,z) 解: (1). x(P(x,z) Q(y) (y)S(x,y) u(P(u,z) Q(y) (v)S(x,v) (2). (x)(P(x) Q(x) (R(x)
5、 (z)S(x,z) (y)(P(y) Q(y) (R(x) (z)S(x,z)习题习题 2.5:?2.4? 解:(1).x(P(x,z) Q(y) (y)S(x,y) x(P(x,z) Q(u) (y)S(v,y)(2).(x)(P(x) Q(x) (R(x) (z)S(x,z) (x)(P(x) Q(x) (R(y) (z)S(y,z)习题习题 2.6:?解?I1? (x)(P(x) Q(x)?(x)(P(x) Q(x) ?I1? 解:I1: D?;P(x)x:?; Q(x) : x?. ?解?(x)(P(x) Q(x)? ?,(x)(P(x) Q(x)? (1). ?解?I2? (x)(
6、P(x) Q(x)?(x)(P(x) Q(x) ?I2?习题习题 2.7:?解?I?解?I? ? (1). (x)A(x) (x)B(x) (x)(A(x) B(x)2(2). (x)A(x) (x)B(x) (x)(A(x) B(x) 解:I: D?;P(x)x:?; Q(x) : x?. ?解?(1),(2)? ?,?, ?(1),(2)?,?.习题习题 2.8:? (1). (x)(P(x) (y)Q(x,y) (2). (x)(P(x) (y)Q(y) (3). (x)(y)P(x,y) (z)Q(z) R(x) (4). (x)P(x,y) (y)Q(y) (z)R(z) 解: (1
7、). (x)(P(x) (y)Q(x,y) (x)(y)(P(x) Q(x,y) (2). (x)(P(x) (y)Q(y) (x)(P(x) (y)Q(y) (x)(P(x) (y)Q(y) (x)(P(x) (y)Q(y) (x)(P(x) (y)Q(y) (x)(y)(P(x) Q(y) (x)(y)(P(x) Q(y) (3). (x)(y)P(x,y) (z)Q(z) R(x) (x)(y)P(x,y) (z)(Q(z) R(x) (x)(z)(y)P(x,y) (Q(z) R(x) (x)(z)(y)(P(x,y) (Q(z) R(x) (x)(z)(y)(P(x,y) (Q(z)
8、 R(x) (4). (x)P(x,y) (y)Q(y) (z)R(z) (x)P(x,u) (y)Q(y) (z)R(z) (x)(P(x,u) (y)Q(y) (z)R(z) (x)(y)(P(x,u) Q(y) (z)R(z) (x)(y)(P(x,u) Q(y) (z)R(z) (x)(y)(P(x,u) Q(y) (z)R(z) (x)(y)(P(x,u) Q(y) (z)R(z) (z)(x)(y)(P(x,u) Q(y) R(z) (z)(x)(y)(P(x,u) Q(y) R(z) (z)(x)(y)(P(x,u) Q(y) R(z) (z)(x)(y)(P(x,u) Q(y)
9、 R(z) (x)(y)(z)(P(x,u) Q(y) R(z)习题习题 2.9:? (1). ?(x)(P(x) Q(x)?(x)P(x) 解:?: ?D?, P(x):x?, Q(x):x?. ? ?. ?:?. (2). ?(x)P(x),(x)Q(x)?(x)(P(x) Q(x) 解:?. ?:3? (1)(x)P(x)P (2)P(a)T(1) ES? (3)P(a) Q(a)T(2)? (4)(x)(P(x) Q(x)T(3)EG?习题习题 2.10:? (1). ? ? 解:?,?D ?, ?: M(x):x? ?; R(x):x?; O(x):x?; ?: H1: (x)R(x) M(x); H2: R(x) O(x); H3: (x)O(x); C : (x)M(x) ?: ? (1)(x)O(x)P (2)(x)O(x)T(1) ? (3)O(a)T(2)ES? (4)R(x) O(x)P (5)R(a) O(a)T(4) I (6)R(a)T(3)(5)? (7)(x)R(x) M(x)P? (8)R(a) M(a)T(7)US? (9)M(a)T(6)(8)? (10)(x)M(x)T(9)EG?(2). a ?习?习? ?习?习?习题习题 2.11:?:(x)A(x) (x)B(x) ()(A(x) B(x)4
