Let A= x: P(x) and B= x: Q(x) Prove that if for all x: P(x) = > Q(x) then A is a subset of B.

Let A= x: P(x) and B= x: Q(x)Prove that if for all x, P(x) implies Q(x) then A is a subset of B.

Let x be any object and suppose that it is a subset of A. Then P(x) must be true for all x, and since for all x, P(x) implies Q(x) then x is a subset of B. So therefore, A is a subset of B.~~~~