a) Let N(x) be the predicate x is a tram, M(x) be the predicate x is...

 

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a) Let N(x) be the predicate "x is a tram", M(x) be the predicate "x is a horse", and H(x, y) be the predicate "x runs faster than y". Express the statement "There are some trams that are slower than horses." using predicate logic. (5 Points) b) Rewrite the statement -(Vy Q(y) xP(x)) so that all negation symbols immediately precede predicates. For instance, -VxP(x) should be rewritten as 3x-P(x) so that "-" immediately precedes P(x). (5 Points) c) Consider two predicates P(x), Q(x) with the same universe of discourse. Prove that (Vx(P(x) Q(x)) VyQ(y)) xP(x) (5 Points) d) Is the proposition Vyx P(x, y) x Vy P(x, y) always a tautology for any predicate P(x, y)? Justify your answer. (5 Points) Activate Windows a) Let N(x) be the predicate "x is a tram", M(x) be the predicate "x is a horse", and H(x, y) be the predicate "x runs faster than y". Express the statement "There are some trams that are slower than horses." using predicate logic. (5 Points) b) Rewrite the statement -(Vy Q(y) xP(x)) so that all negation symbols immediately precede predicates. For instance, -VxP(x) should be rewritten as 3x-P(x) so that "-" immediately precedes P(x). (5 Points) c) Consider two predicates P(x), Q(x) with the same universe of discourse. Prove that (Vx(P(x) Q(x)) VyQ(y)) xP(x) (5 Points) d) Is the proposition Vyx P(x, y) x Vy P(x, y) always a tautology for any predicate P(x, y)? Justify your answer. (5 Points) Activate Windows