1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Dec 11, 2011 #1
    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(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.
     
  2. jcsd
  3. Dec 11, 2011 #2

    eumyang

    User Avatar
    Homework Helper

    A set A of k elements has k(k-1)/2 subsets of two elements, as you said.
    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?
     
  4. Dec 11, 2011 #3
    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(k-1)/2 = k

    So, how can we argue that this will solve the problem ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A set A of n elements has n(n-1)/2 subsets of 2 elements
Loading...