Let ∗ be a binary operation on the set Q of rational numbers as follows: a ∗ b = a 2 + b 2 Find which of the binary operations are commutative and which are associative.

Question

Philoid · Accepted Answer

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.

Let ∗ be a binary operation on the set Q of rational numbers as follows:a ∗ b = a2 + b2Find which of the binary operations are commutative and which are associative.

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.