Set Theory

Question

If A = {1, 3,5,7,.......}

Then (A, +) is semi group or not.

 

Doubt :

a +(b+c) =( a + b) +c

So associativity property is present

But a + b  doesn't belong to A

So closure property is not present.

 

 

So A is semi group or not.

Comments

to check associativity will have to check closure property first, so it isn’t a semigroup