Let n be an integer Prove the following If 5n 1 is odd then

Let n be an integer. Prove the following If 5n + 1 is odd, then n is even. with, proof by contrapositive.

Solution

To use contrapositive, we have to prove \"if n is not even, 5n+1 is not odd\"

If n is not even, n is odd. An odd mutplied by odd is always an odd.

And odd+odd (1) gives an even ( not odd)

Hence, 5n+1 is not odd.

<Hence, proved>