Question:
Show that the set $A=\{-1,0,1)$ is not closed for addition.
Solution:
For a set to be closed for addition,
For any 2 elements of the set, say a and $b, a+b$ must also be a member of the given set, where a and $\mathrm{b}$ may be same or distinct
In the given problem let $a=1$ and $b=1$
$a+b=2$ which is not in the given in set
So the set is not closed for addition.
Hence proved.