# Use induction to prove that for a finite set A of cardinality n, there are n(n+1)/2 distinct 2-element subsets of A. ?

Update:

i meant n-1

### 1 Answer

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- az_lenderLv 71 month ago
Let's start with a set A that has only two elements. Then

n(n+1)/2 = 2*3/2 = 3.

And hence, your proposition is obviously false. There is only one 2-element subset of A.

I think you should've said n(n-1)/2.

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