13. Let A, B and C be non-empty sets. (a) Prove that A (B ∩ C) = A (B ∩ C) (b) Give a counterexample to show that the following is not true. P(A ∪ B) = P(A) ∪ P(B)
Added by Nathan R.
Step 1
First, let x be an arbitrary element in A (B ∩ C). This means that x is in A and also in the intersection of B and C. In other words, x is in A, B, and C. Therefore, x is also in A and in the intersection of B and C, which is the right-hand side of the equation. Show more…
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