# Answer to Question #10821 in Discrete Mathematics for Manoj Choudhary

Question #10821

Let E = {2, 4, 6, …}. Then prove that (E, +) is a semigroup, where + is usual addition.

Expert's answer

To prove it, we should check a semigroup axiom, that for any a,b \in E a+b \in E

too. It's obvious, because a summ of two even numbers will always be an even

number too, so it will belong to E. The statement is proved.

too. It's obvious, because a summ of two even numbers will always be an even

number too, so it will belong to E. The statement is proved.

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