Question

Which of the following sets is NOT closed under addition.

A) Natural Numbers
B) Whole numbers
C) Integers
D) Odd numbers

Answer 1

Explanation:

The odd numbers.

Suppose you have 31 and 27 when you add these two together, you get 58 which is not an odd number.

If you need a more mathematical proof, you could do it this way.

2x+1

2x is even. Anything multiplied by 2 is even. When you add 1 you get an odd number

So continue on

2y + 1 is the other number.

2x + 1 + 2y + 1 = 2(x + y) + 2

2 (x + y ) is even. When you add 2 to it, nothing changes. The result is still even.