**Closure Property w.r.t “*“**

**Definition**: A non-empty set G having binary operation “*” (say) is called **group** in math if it satisfies the following axioms:

i.e, a\ast b\in G\;\;\;\;\;\;\;\forall\;a,b\in G

**Associative Law w.r.t “*“**

**Identity element exist.**

There is identity element e in G such that

a\ast e=e\ast a=a\;\;\;\;\;\;\;\;\forall\;a\in G**Inverse of each element exist.**

For each a\in G there is an a^{-1}\in\;G such that

you can also check semi group and monoid