1. Suppose S is a set of universes and A, B is a subset of S. Prove the following statement that A B = A Bc
2. Prove using the table of truth that [p (p q)] q is a tautology.
3. Suppose R is a set of real numbers and R is a relation to R where for each a, b R, aRb if and only if a b is divisible by 4. Prove that R is an equivalent relation to R .
4. Suppose f: R R and g: R R with f(x) = x 2 4 and g(x) = 5 2x. Specify f. g and the region of origin of (D(f. g)).
5. Suppose f: R R and g: R R with f(x) = 4x 2 and g(x) = 3x 2 4. Specify a. compositional functions of f and g, (f g) and their domains. b. inverse of f, (f1).
6. Prove by using mathematical induction that n3 + 2n is divisible by 3 for each n .