Commutative Binary Operations on Sets of 2 and 3 Elements

[tgt]

Homework Statement

How many different commutative binary operations can be defined on a set of 2 elements? On a set of 3 elements?

The Attempt at a Solution

I do not understand the question. Seems like an infinite number.

 

[Dick]

If '*' is the operation and {a,b} is the set of two elements, then to define the operation you need to define a*a, a*b, b*a and b*b in the set {a,b}. That's hardly an infinite number of possibilities.

 

[tgt]

If '*' is the operation and {a,b} is the set of two elements, then to define the operation you need to define a*a, a*b, b*a and b*b in the set {a,b}. That's hardly an infinite number of possibilities.

Got it. Just confused at the time.