In: Advanced Math
Prove that if n is an integer and n^2 is even the n is even.
Sol.- Let n is an integer and is even.
To prove:- n is even
We will prove it by using method of contradiction.
Let us assume that n is an integer and is even but n is not even.i.e. n is odd.
Since n is odd
n = 2k + 1 , for some integer k.
[on squaring both sides]
which is not possible since is even.
So, this contradicts that the fact is even.
Hence our assumption that n is not even is wrong.
Thus, if n is an integer and is even then n is also even. Hence Proved.