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Determine whether each of the following operations define a binary operation on the given set or not:
‘*’ on Q defined by for all a,b Q.
Given that ‘*’ is an operation that is valid in the Rational Numbers ‘Q’ and it is defined as given:
⇒ , where a,b∈Q
Since a∈Q and b∈Q,
According to the problem it is given that on applying the operation ‘*’ for two given rational numbers it gives a rational number as a result of the operation,
⇒ a*b∈Q ...... (1)
Let the value of b = – 1 and a = 2
∴ the operation ‘*’ does not define a binary operation on Q.
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