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Suppose that D and E are sets, and D ? E. Let A = P(E)....

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Advance Math

Suppose that D and E are sets, and D ? E. Let A = P(E). Recallthat P(E) denotes the set of all subsets of E. Define a relation Ron A by

R = {(X, Y) ? A × A: [(X ? Y) ? (Y ? X)] ? D}. So, XRY if andonly if [(X?Y) ? (Y ?X)] ? D.

Prove that R is an equivalence relation on A.

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