Let ∗ be a binary operation on the set Q of rational numbers as follows:
a ∗ b = a2 + b2
Find which of the binary operations are commutative and which are associative.
It is given that ∗ be a binary operation on the set Q of rational numbers is defined as
a ∗ b = a2 + b2
For a, b ϵ Q, we get,
a * b = a2 + b2 = b2 + a2 = b * a
⇒ the operation is commutative.
We can see that (1 * 2) * 3 ≠ 1 *(2 * 3), where 1,2,3 ϵ Q
Therefore, the operation * is not associative.