Show that the set

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.

 

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