Closure Property w.r.t “” Definition: A non-empty set G having binary operation “*” (say) is called group in math if

Completing the Square examples: Sometimes, the quadratic polynomials are not easily factorable. For Example, consider It is difficult to make

Order of a Group: The order of group  is the number of elements present in that group , also say it’s cardinality.

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

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