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Question
Determine whether * is a binary operation on the sets-given below.
(a * b) = `"a"sqrt("b")` is binary on R
Solution
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.
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