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Main Question or Discussion Point
Prove by induction that the number of 2-subsets of an n-set A equals n(n-1)/2.
Not sure why you want to use induction to do this but here you go in a fast and loose manner:Prove by induction that the number of 2-subsets of an n-set A equals n(n-1)/2.
Yes That gives a direct formula but what the poster needed was a step for an inductive proof which is what Rodigee gave since the new element (n+1) combines with the first n elements to form n more sets of two elements.if so, it is easy to see that the first combine with n-1 elements, the second with n-2 elements, and so on