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Prove the following: Theorem. Let X be a set and {Xi ⊆ X : i ∈...

Prove the following: Theorem. Let X be a set and {Xi ⊆ X : i ∈ I} be a partition of X. Then R = { (x1, x2) ∈ X × X : ∃i ∈ I,(x1 ∈ Xi) ∧ (x2 ∈ Xi) } is an equivalence relation on X.

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