Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?


CLEAR CHECK

Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.


Look at these different examples: 3 + 5 = 8, 13 + 5 = 18, 23 + 5 = 28. So the sum of two odd numbers must be even.


Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.


Every time you add two odd numbers, the sum is an even number.