Consider the following statement. For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅.

Question

Let the universal set U be {1, 2, 3, 4, 5}, and assume that all sets are subsets of U. Is the statement true or false? Find subsets of {1, 2, 3, 4, 5} that can be used to answer this question. (Enter the sets as A, B, and C in a comma-separated list. Use set-roster notation or write EMPTY or ∅ for the empty set.)

A, B, C = (_____)

Answer 1

A = {1,2,3,4}

B={1}

C={2}

A-B = {2,3,4}

A-C = {1,3,4}

the intersection is {3,4} is not empty