For each of the following claims, decide whether you think the statement is true for all sets of integers A, B,C. If it’s true for every A, B,C, then explain why. (A Venn diagram may be helpful.) If...

For each of the following claims, decide whether you think the statement is true for all sets of integers A, B,C. If it’s true for every A, B,C, then explain why. (A Venn diagram may be helpful.) If it’s not true for every A, B,C, then provide an example for which it does not hold.

1. A ∩ B = ∼(∼A ∪ ∼B)

2. A ∪ B = ∼(∼A ∩ ∼B)

3. (A − B) ∪ (B − C) = (A ∪ B) − C

4. (B − A) ∩ (C − A) = (B ∩ C) − A