Question: Given a set S, define a pair in S to be a subset of S containing exactly 2 elements. (For example, the set {1, 2,

Given a set S, define a pair in S to be a subset of S containing exactly 2 elements. (For example, the set {1, 2, 3} contains the pairs {1, 2}, {1, 3}, and {2, 3}.) Prove by weak induction (without using combinatorics formulas) that: any set with n elements has exactly n(n1) 2 different pairs, when n is an integer greater than or equal to 2

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