Question

Determine whether * is a binary operation on the sets-given below.

(a * b) = `"a"sqrt("b")` is binary on R

Answer 1

No.

* is not a binary operation on R.

Reason: a, b ∈ R.

⇒ b can be -ve number also and the square root of a negative number is not real.

So `sqrt("b")` ∉ R even when b ∈ R.

So `sqrt("b")` ∉ R.

ie., a * b ∉ R.

* is not a binary operation on R.