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

Suppose that D and E are sets, and D ⊆ E. Let A = P(E). Recall that P(E) denotes the set of all subsets of E. Define a relation R on A by

R = {(X, Y) ∈ A × A: [(X − Y) ∪ (Y − X)] ⊆ D}. So, XRY if and only if [(X−Y) ∪ (Y −X)] ⊆ D.

Prove that R is an equivalence relation on A.

Expert Solution

Colby Messinger answered 1 year ago

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

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