Monoid, Definition and Examples :-

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

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

$(a\ast b)\ast c=a\ast(b\ast c)\;\;\;\;\;\;:\;\forall\;a,b,c\in G$

There is identity element e in G such that

$a\ast e=e\ast a=a\;\;\;\;\;\;\;\;\forall\;a\in G$

If the above three properties hold then the set is called Monoid.

We can also say semi group having identity element is called Monoid

Examples: Monoid

The following sets are Monoid