## Consider the statement. For all sets A, B, and C, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). Fill in the blanks in the following proof for the stateme

Question

Consider the statement. For all sets A, B, and C, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). Fill in the blanks in the following proof for the statement. (In the proof, let ∩ and ∪ stand for the words “intersection” and “union,” respectively.) Proof: Suppose A, B, and C are any sets. [To show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C), we must show that A ∩ (B ∪ C) ⊆ (A ∩ B) ∪ (A ∩ C) and that (A ∩ B) ∪ (A ∩ C) ⊆ A ∩ (B ∪ C).]

Proof that A ∩ (B ∪ C) ⊆ (A ∩ B) ∪ (A ∩ C): Let x ∈ A ∩ (B ∪ C).

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Math
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2021-09-10T18:49:09+00:00
2021-09-10T18:49:09+00:00 1 Answer
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## Answers ( )

Answer:By definition it follows that

Step-by-step explanation:by definition

Then it follows that

The other side is pretty much the same.