Prove that if a is odd, then a + 2 is odd. Solution Let a be odd Then a is of the form 2n+1 where n is an integer Consider a+2 a+2 = 2n+1+2 = 2(n+1)+1 = 2m+1 where m = n+1 is an integer. Hence a+2 is of the form 2m+1 which when divided by 2 gives remainder 1. Hence a+2 is odd if a is odd..