( )不是有效的推理。
A: 前提:("x)(H(x)ÞM(x)) 结论:("x)("y)(H(y)∧N(x, y))Þ($y)(M(y)∧N(a, y))
B: 前提:("x)(G(x)ÞH(x)),~($x)(F(x)∧H(x)) 结论:($x)F(x)Þ($x)G(x)
C: 前提:("x)(P(x)ÞQ) 结论:("x)P(x)ÞQ
D: 前提:("x)P(x)∨("x)Q(x) 结论:("x)(P(x)∨Q(x))
A: 前提:("x)(H(x)ÞM(x)) 结论:("x)("y)(H(y)∧N(x, y))Þ($y)(M(y)∧N(a, y))
B: 前提:("x)(G(x)ÞH(x)),~($x)(F(x)∧H(x)) 结论:($x)F(x)Þ($x)G(x)
C: 前提:("x)(P(x)ÞQ) 结论:("x)P(x)ÞQ
D: 前提:("x)P(x)∨("x)Q(x) 结论:("x)(P(x)∨Q(x))
举一反三
- ( )不是有效的推理。 A: 前提:("x)(~P(x)ÞQ(x)), ("x)~Q(x)结论:P(a) B: 前提:("x)(P(x)ÞQ) 结论:("x)P(x)ÞQ C: 前提:("x)(P(x)∨Q(x)), ("x)(Q(x)Þ~R(x)) 结论:($x)(R(x)ÞP(x)) D: 前提:("x)(P(x)Þ(Q(x)∧R(x))), ($x)(P(x)∧S(x))结论:("x)(R(x)∧S(x)) E: 前提:("x)($y)P(x, y)结论:("x)($y)($z)(P(x, y)∧P(y, z)) F: 前提:("x)P(x)∨("x)Q(x)结论:("x)(P(x)∨Q(x)) G: 前提:("x)(G(x)ÞH(x)),~($x)(F(x)∧H(x))结论:($x)F(x)Þ($x)G(x) H: 前提:("x)(H(x)ÞM(x))结论:("x)("y)(H(y)∧N(x, y)) Þ ($y)(M(y)∧N(a, y) )
- ( )不是有效的推理。 A: 前提:("x)(~P(x)ÞQ(x)), ("x)~Q(x)结论:P(a) B: 前提:("x)(P(x)ÞQ) 结论:("x)P(x)ÞQ C: 前提:("x)(P(x)∨Q(x)), ("x)(Q(x)Þ~R(x)) 结论:($x)(R(x)ÞP(x)) D: 前提:("x)(P(x)Þ(Q(x)∧R(x))), ($x)(P(x)∧S(x))结论:("x)(R(x)∧S(x)) E: 前提:("x)($y)P(x, y)结论:("x)($y)($z)(P(x, y)∧P(y, z)) F: 前提:("x)P(x)∨("x)Q(x)结论:("x)(P(x)∨Q(x)) G: 前提:("x)(G(x)ÞH(x)),~($x)(F(x)∧H(x))结论:($x)F(x)Þ($x)G(x) H: 前提:("x)(H(x)ÞM(x))结论:("x)("y)(H(y)∧N(x, y)) Þ ($y)(M(y)∧N(a, y) )
- 构造下列推理的证明。 (1)前提:$xF(x),"x((F(x)∨G(x))→H(x));结论:$xH(x)。 (2)前提:$xF(x)∧"xG(x);结论:$x(F(x)∧G(x))。 (3)前提:¬$xF(x),"x($y(G(x,y)∧P(y))→$y(F(y)∧R(x,y)));结论:"x"y(G(x,y)→¬P(y))。
- 3.4对下列各题分别证明G是否为F1,F2,…,Fn的逻辑结论:(1)F:(Ǝx)(Ǝy)(P(x,y)G:(ꓯy)(Ǝx)(P(x,y)(2)F:(ꓯx)(P(x)∧(Q(a)∨Q(b)))G:(Ǝx)(P(x)∧Q(x))(3)F:(Ǝx)(Ǝy)(P(f(x))∧(Q(f(y)))G:P(f(a))∧P(y)∧Q(y)(4)F1:(ꓯx)(P(x)→(ꓯy)(Q(y)→[img=1x1]17e0a6a55067d30.gif[/img]L(x.y)))F2:(Ǝx)(P(x)∧(ꓯy)(R(y)→L(x.y)))G:(ꓯx)(R(x)→[img=1x1]17e0a6a55067d30.gif[/img]Q(x))(5)F1:(ꓯx)(P(x)→(Q(x)∧R(x)))F2:(Ǝx)(P(x)∧S(x))G:(Ǝx)(S(x)∧R(x))
- 对谓词公式(∀x)((∃y)﹁P(x,y)∨(∃y)( Q(x,y) ∧﹁R(x,y)))化简可以得到包含哪几项的子句? A: P(x,f(x))∨Q(x,g(x)) B: ﹁P(x,f(x))∨Q(x,g(x)) C: ﹁P(y,f(y))∨﹁R(y,g(y)) D: P(y,f(y))∨R(y,g(y))