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A set A of n elements has n(n1)/2 subsets of 2 elements 
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#1
Dec1111, 12:59 PM

P: 10

I would very much like some help to the following problem.
1. The problem statement, all variables and given/known data Using mathematical induction, prove that a finite set A of n elements has n(n1)/2 subsets of two elements. 3. The attempt at a solution * Base step n=2: 2(21)/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(k1)/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+11)/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. 


#2
Dec1111, 01:26 PM

HW Helper
P: 1,347

Suppose you add a new element to set A. How many new subsets can be created where one of the elements of these subsets is the new element? 


#3
Dec1111, 01:46 PM

P: 10

if we add an element to the set which previously had k elements (that is now has k+1 elements) the new subsets that include the new element will be :
(k+1)k/2  k(k1)/2 = k So, how can we argue that this will solve the problem ? 


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