Open Logic Project - Sets Problems

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Reference no: EM132380987

Open Logic Project - Sets Problems

Problem 1 - Show that there is only one empty set, i.e., show that if X and Y are sets without members, then X = Y.

Problem 2 - List all subsets of {a, b, c, d}.

Problem 3 - Show that if X has n elements, then ρ(X) has 2n elements.

Problem 4 - Prove rigorously that if X ⊆ Y, then X U Y = Y.

Problem 5 - Prove rigorously that if X ⊆ Y, then X ∩ Y = X.

Problem 6 - List all elements of {1, 2, 3}3.

Problem 7 - Show, by induction on k, that for all k ≥ 1, if X has n elements, then Xk has nk elements.

Reference no: EM132380987

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