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.

   Hint (a):

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

   Partial Answer (a):

   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.

   Hint (b):

   What happens if you mulitply two even numbers together?

   Partial Answer (b):

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