Is this set closed under addition or multiplication or both and why? $\{-1,0,1\}$
Please give an explanation and also tell me what does closed under addition and multiplication mean. 
Different definitions are given everywhere.

A set $X$ is closed under addition if $x+y\in X$ for any $x,y\in X$. It is closed under multiplication if $x\times y\in X$ for any $x,y\in X$. Note that $x$ and $y$ may or may not be equal.
The set $\{-1,0,1\}$ is closed under multiplication but not addition (if we take usual addition and multiplication between real numbers). Simply verify the definitions by taking elements from the set two at a time, possibly the same.
