习题五求下列谓词公式得子句集。(1) $x$y(P(x,y) ÙQ(x,y))解:去掉存在量词变为:P(a,b)ÙQ(a,b) 变成子句集{ P(a,b),Q(a,b)}(2) "x "y(P(x,y) ®Q(x,y))解:去掉蕴涵符号变为:"x "y(¬ P(x,y) Ú Q(x,y))去掉全称量词变为:¬ P(x,y) Ú Q(x,y)变成子句集{ ¬ P(x,y) Ú Q(x,y)}(3) "x$y((P(x,y) ÚQ(x,y)) ®R(x,y))解:去掉蕴涵符号变为:"x $y(¬ (P(x,y) Ú Q(x,y)) Ú R(x,y))否定符号作用于单个谓词变为:"x $y((¬ P(x,y) Ù¬ Q(x,y)) Ú R(x,y))去掉存在量词变为:"x ((¬ P(x,f(x)) Ù¬ Q(x,f(x))) Ú R(x,f(x)))去掉全称量词变为: (¬ P(x,f(x)) Ù¬ Q(x,f(x))) Ú R(x,f(x)化合取范式为:(¬ P(x,f(x)) Ú R(x,f(x))Ù(¬ Q(x,f(x)) Ú R(x,f(x))变元:(¬ P(x,f(x)) Ú R(x,f(x)))Ù(¬ Q(y,f(y)) Ú R(y,f(y)))变成子句集{ ¬ P(x,f(x)) Ú R(x,f(x)), ¬ Q(y,f(y)) Ú R(y,f(y))}(4) "x (P(x) ®$y (P(y) ÙR(x,y)))解:去掉蕴涵符号变为:"x (¬ (P(x) Ú $y (P(y) ÙR(x,y)))去掉存在量词变为:"x (¬ (P(x) Ú (P(f(x)) ÙR(x,f(x)))去掉全称量词变为: (¬ (P(x) Ú (P(f(x)) ÙR(x,f(x)))化合取范式为:(¬ (P(x) Ú P(f(x))) Ù(¬ (P(x) ÚR(x,f(x)))变元:(¬ (P(x) Ú P(f(x))) Ù(¬ (P(y) ÚR(y,f(y)))变为子句集:{¬ (P(x) Ú P(f(x)),¬ (P(y) ÚR(y,f(y))}(5) $x(P(x) Ù"x(P(y) ®R(x,y)))解:去掉蕴涵符号变为:$x(P(x) Ù"x(¬P(y) ÚR(x,y)))去掉存在量词变为:P(a) Ù"x(¬P(y) ÚR(a,y))去掉全称量词变为:P(a) Ù (¬P(y) ÚR(a,y))变成子句集:{ P(a) ,¬P(y) ÚR(a,y) }(6) $x$y"z $u"v $w(p(x,y,z,u,v,w) Ù(Q(x,y,z,u,v,w) Ú¬R(x,z,w)))解:去掉存在量词变为: "z "v (p(a,b,z,f(z),v,g(z,v)) Ù(Q(a,b,z,f(z),v, g(z,v) Ú¬R(a,z, g(z,v)))去掉全称量词变为:p(a,b,z,f(z),v,g(z,v)) Ù(Q(a,b,z,f(z),v, g(z,v) Ú¬R(a,z, g(z,v))变元:p(a,b,x,f(x),y,g(x,y)) Ù(Q(a,b,z,f(z),v, g(z,v) Ú¬R(a,z, g(z,v))化成子句集:{p(a,b,x,f(x),y,g(x,y)) , Q(a,b,z,f(z),v, g(z,v) Ú¬R(a,z, g(z,v)) }3、 试推断下列子句集中哪些就是不可满足得。(1) S={P(y) Ú¬Q(y), ¬P(f(x)) ÚQ(y)}解:（1）P(y) Ú¬Q(y)（2）¬P(f(x)) ÚQ(z) (适当改名使子句之间不含相同变...
