Explanation:
A set is "closed" for a particular operation if performing that operation on members of the set always gives a member of the set.
<u>closed example</u>
For example, the set {0, 1} is <em>closed for multiplication</em>:
0 × 0 = 0
0 × 1 = 0
1 × 1 = 1 . . . all result values are members of the set
Performing multiplication on any two members of the set gives a member of the set.
__
<u>not closed example</u>
The same set {0, 1} is <em>not closed for addition</em>:
0 +0 = 0
0 +1 = 1
1 +1 = 2 . . . not a member of the set
Performing addition on any two members of the set does not always give a member of the set.
_____
<em>Additional comment</em>
Sometimes you are asked to demonstrate closure of a particular set using a particular example. As we see with <em>addition</em>, above, some examples may seem to demonstrate closure, while another example may prove the set is not closed. In short, you can demonstrate that the set is closed for a particular operation on a particular example, but that does not demonstrate closure in general.