Double Math

Semi Group, Definition and Examples:-

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”.