I would very much like some help to the following problem.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Using mathematical induction, prove that a finite set A of n elements has n(n-1)/2 subsets of two elements.

3. The attempt at a solution

* Base step n=2: 2(2-1)/2= 1 subset of two elements.

* Inductive step: assuming the statement holds for n=k, that is a set A of k elements has k(k-1)/2 (hypothesis)

We want to show that it also holds for n=k+1, that is a set A of k+1 has (k+1)(k+1-1)/2 elements.

How can we infer from the hypothesis ??? I have no idea ...

I have an engineering background so be as descriptive as you can.

Thank you in advance.

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# A set A of n elements has n(n-1)/2 subsets of 2 elements

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