Question

Give a direct proof that the sum an even integer and an odd integer is odd.

Answer 1

Even integer: 2 x a, where a is a  natural number without 0;
Odd integer : 2 x b + 1 , where b is a natural number;
So, 2 x a + 2 x b+ 1 = 2 x ( a + b ) + 1, which is an odd integer.