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 $A$ is closed under a binary operation $\star: A \times A \longrightarrow A$ if for all $a, b \in A$, $a \star b \in A$. In other words, performing the binary operation on any two elements of the set always gives you back something that is also in the set.
So in this case, closure under addition means $a + b \in \{-1, 0, 1\}$ for all $a, b \in \{-1, 0, 1\}$. This set isn't closed under addition; consider $1 + 1$.
Closure under multiplication in this case means $ab \in \{-1, 0, 1\}$ for all $a, b \in \{-1, 0, 1\}$. This set is closed under multiplication; simply write out all possible products of elements.
