与公式("x)(P(x)∧Q(x, y))Þ($x)R(x, y)等值的是( )。
A: ("x)(P(x)∧Q(x, z))Þ($x)R(x, y)
B: ("y)(P(y)∧Q(y, y))Þ($x)R(x, y)
C: ("z)(P(z)∧Q(x, y))Þ($x)R(x, y)
D: ("u)(P(u)∧Q(u, z))Þ($x)R(x, z)
A: ("x)(P(x)∧Q(x, z))Þ($x)R(x, y)
B: ("y)(P(y)∧Q(y, y))Þ($x)R(x, y)
C: ("z)(P(z)∧Q(x, y))Þ($x)R(x, y)
D: ("u)(P(u)∧Q(u, z))Þ($x)R(x, z)
举一反三
- 【单选题】与公式("x)(P(x)∧Q(x, y))Þ($x)R(x, y)等值的是()。 A. ( " x )( P ( x ) ∧ Q ( x , z )) Þ ( $ x ) R ( x , y ) B. ( " y )( P ( y ) ∧ Q ( y , y )) Þ ( $ x ) R ( x , y ) C. ( " z )( P (z ) ∧ Q ( x , y )) Þ ( $ x ) R ( x , y ) D. ( " u )( P ( u ) ∧ Q ( u , z )) Þ ( $ x ) R ( x , z )
- ( )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) )
- 将公式∀x(P(x)→Q(x,y))∧R(x,y)使用改名规则变换后正确的是 。 A: ∀z(P(z)→Q(z,y))∧R(x,y) B: ∀y(P(y)→Q(y,y))∧R(x,y) C: ∀z(P(z)→Q(x,y))∧R(x,y) D: ∀z(P(z)→Q(z,y))∧R(z,y)
- 以下哪几项是前束范式? A: (∀x)(∀y)(P(x)∧(∃z)Q(y,z)∨R(x,z)) B: (∀z)(∀x)(∃y)(P(x)∧Q(y,z)∨R(x,z)) C: (∀x)(∀y)(P(x)∧Q(y,z)∨(∃z)R(x,z)) D: (∃x)(∃y)(∀z)(P(x)∧Q(y,z)∨R(x,z))
- 谓词公式∀xP(x)→∀xQ(x)∨∃yR(y)的前束范式为 A: ∀x∀z∃y(P(x)→Q(z) ∨ R( y)) B: ∃x∀z∃y(P(x)→Q(z) ∨ R( y)) C: ∀x∃y(P(x)→Q(x) ∨ R( y)) D: ∃x∀y(P(x)→Q(x) ∨ R( y))