Consider the three sets from = LETTERS: A = {U, X, M, J, B, D}, B = {N, J, H, C, G, X}, and

Consider the three sets from Ω = LETTERS: A = {“U”, “X”, “M”, “J”, “B”, “D”}, B = {“N”, “J”, “H”, “C”, “G”, “X”}, and C = {“H”, “V”, “N”, “K”,“D”, “F”}. Using the operators intersect and union, for the sets A, B, and C, verify the following:

1. (A ∩ B)′ = A′ ∪ B′ and (A ∪ B)′ = A′ ∩ B′.

2. (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) and (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C).

3. Using the sample function, verify (i) and (ii) for arbitrary sets A, B, and C.