Consider finite sets A, B, C. For the following statements, prove it if it is true, or disprove it if it is false. (a) (4 pts) AU (BOC) = (AUB) n(AUC). (Hint: First prove "if z EAU (BOC), then TE (AUB) n(AUC)". Then prove "if a (AUB) n(AUC), then x EAU (BNC)".) (b) (4 pts) An B||A|-|B. (c) (4 pts) A\B|2|A|-|B|. (d) (4 pts) |A|+|B| = |AU B| if and only if A and B are disjoint. (e) (4 pts) AUBUC| = |A|+|B|+|C|-|AnB|-|AnC|-|BnC|+|AnBnC). (f) (4 pts) If f: A B is a bijection, and g: B C is a bijection, then h: A C defined as h(x) = g(f(x)) is a bijection. (g) (4 pts) Consider any functions f: A B and g: B C (which may or may not be bijections). If h: AC defined as h(x) = g(f(x)) is a bijection, then both f and g must be bijections.