Question: (a) Why is A A for every set A? (b) Given sets A and B, explain why A B is equivalent to asserting B A.

(a) Why is A A for every set A?

(b) Given sets A and B, explain why A B is equivalent to asserting B A.

(c) For three sets A,B, and C, show that A B and B C implies A C.

These three properties are what is meant by saying that is an equivalence

relation.

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