Let S ⊆ ℕ and let x ∈ S. We say that x is a minimum element of S if for every y ∈ S, x ≤ y. a) Suppose that S has a minimum element. Prove that this minimum element is unique. b) Prove that if S ⊆ ℕ is nonempty, then S has a minimum element. Hint: For n ∈ ℕ, let P(n) be the statement “If n ∈ S, then S has a minimum element.” Prove that P(n) is true for every n

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