6.2 Semigroups, monoids and groups 6.2.1 Semigroups, monoids Definition 5: A semigroup S; is a nonempty set together with a binary operation satisfying associative law. Definition 6: A monoid is a semigroup [ s; a that has an identity.6.2 Semigroups,monoids and groups • 6.2.1 Semigroups, monoids • Definition 5: A semigroup [S;] is a nonempty set together with a binary operation  satisfying associative law. • Definition 6: A monoid is a semigroup [S; ] that has an identity