Prove that |P₂(Aₙ)| = n(n-1)/2 by induction

[ssome help]

Let A(subn) = {1,2,3,...,n} For any set B, let P(subk)B=the set of all subsets of B with exactly k elements. For example, P(sub2)({1,2,3})={{1,2},{1,3},{2,3}}.

A) Find P(sub2)(A(sub1)), P(sub2)(A(sub2)), P(sub2)(A(sub4)), and P(sub2)(A(sub5))

B) Use mathematical induction to prove that the number of elements in P(sub2)(A(subn)) is (n*(n-1))/2 for all n elements of Z+.

 

[Evgeny.Makarov]

Re: Mathematic Induction

A) Find P(sub2)(A(sub1)), P(sub2)(A(sub2)), P(sub2)(A(sub4)), and P(sub2)(A(sub5))

The goal of this part of the problem is to make sure you understand the notation and what is being asked. Do you understand it? We would rather not give out a complete solution, and to work together we need to know what you understand. If you have questions about what the problem is asking, then say precisely what is not clear.

Edit: In plain text, it is customary to write A_n for $A_n$. If the subscript consists of more than one character, then you need to surround it by parentheses.