Discrete Mathematics

Question

Prove that for any integer n if 3n+2 is even, then n is even , by method of Contraposition.

Comments

let n = odd, then 2k + 1 = n ,

3n + 2 = 3( 2k + 1 ) + 2 =  6k + 3 + 2 = odd.

Now if n = even = 2k

3n + 2 = (3 * 2k ) + 2 = 6k + 2  = even .

Answer 1

If we take n = odd here, then

3n + 2 = odd always

and If we take n = even here, then

3n + 2 = even always.