Question

show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. is it a monoid under each of the above operations?

Answer 1

A non-empty set S with an operation ∗ i.e., (S,∗) is said to be a semi-group if it satisfies the following axioms.

(1) Closure axiom : a,b∈S⇒a∗b∈S

(2) Associative axiom : (a∗b)∗c=a∗(b∗c),∀a,b,c∈S.

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