CPM Homework Help : INT2 Problem 4-40

Is the set of even numbers closed under addition? That is, if you add two even numbers, do you always get an even number? Is the set of odd numbers closed under addition? Explain your answers.

Hint:

Test out as many different situations as you can. Here are some to test out:

Even $+$ Even
$2+4=$
$8+6=$
$16+20=$
$32+10+4=$
$18+46+12=$

$6$
$14$
$36$
$48$
$76$

Odd $+$ Odd
$3+5=$
$9+7=$
$23+27=$
$19+31+13=$
$17+15+11=$

$8$
$16$
$50$
$63$
$43$

More Help:

What do you think? Do you see any patterns? Make sure you try some numbers of your own.

Answer:

Even numbers are closed under addition. Odd numbers are not. Can you explain why?