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dpesios
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I would very much like some help to the following problem.
Using mathematical induction, prove that a finite set A of n elements has n(n-1)/2 subsets of two elements.
* 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.
Homework Statement
Using mathematical induction, prove that a finite set A of n elements has n(n-1)/2 subsets of two elements.
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.