Semi Group, Definition and Examples:-

1 Comment / Algebra / By Azhar

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

Closure Property w.r.t “ $*$ “

Semi Group

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

Associative Law w.r.t “ $*$ “

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

Examples of Semi Group:

The set of W- {0,1} with respect to “Addition” and “Multiplication”.
The set of Natural Number with respect to “Addition”.
The set of $O^+$ with respect to “Addition”.

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