### Home > AC > Chapter 5 > Lesson 5.2.2 > Problem5-81

5-81.

The Math Notes box for this lesson explains that the set (or group) of odd numbers is closed under multiplication because $(\text{odd})(\text{odd})=\text{odd}$. However, the set of odd numbers is not closed under addition because $(\text{odd})+(\text{odd})\ne\text{odd}$.

1. Examine the set of all even numbers. Is this set closed under addition? Show how you know.

Even numbers are closed under addition, because the sum of two even numbers is also even.

For example,
$4+4=8$
$10+10=20$
$36+36=72$

2. Is the set of even numbers closed under multiplication? Show how you know.

What happens if you mulitply two even numbers together?

For example,
$(4)(4)=16$
$(10)(10)=100$
$(36)(36)=1296$