Step 1:

Let $E=\{2x,x\in N\}$ be the set of ever positive integers.

Closure :Consider $(E,+)$

Let $2x,2y\in E$,then $2x+2y=2(x+y)\in E$

The closure property is satisfied.

Step 2:

Associativity : For $2x,2y,2z\in E$

$(2x+2y)+2z=2x+(2y+2z)$ since these are natural numbers and addition of natural numbers is associative.

$\therefore (E,+)$ is a semi-group.

Step 3:

Consider $(E,.)$

Closure :For $2x,2y,2z\in E$

$(2x)(2y)(2z)=2(4xyz)\in E$

(The product of even numbers is again an even number)

The closure property is satisfied.

Step 4:

Associativity :

The associative property is inherited from the set of natural numbers(as with the associative property of addition over $E$)

Therefore $(E,.)$ is a semi-group.It follows that $E$ is a semi-group under additions as well as multiplication.