Is the binary operation defined for real numbers by: . ?
If are any real numbers, then: . is a real number.
The operation is defined for real numbers.
Is it commutative?
If the operation is commutative, then: .
We have: .
Since , the operation is commutative.
Is it associative?
If the operation is associative, then: .
We have: . not equal
The operation is not associative.