Question

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

Answer 1

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.