Group in Math , Definitions and Examples-Double Math:-

• 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 “*“

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

• 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