Q. 1 G5.0( 1 Vote )

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.

Answer :

Given that ‘*’ is an operation that is valid in the Rational Numbers ‘Q’ and it is defined as given:


, where a,bQ


Since aQ and bQ,


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*bQ ...... (1)


Let the value of b = – 1 and a = 2





the operation ‘*’ does not define a binary operation on Q.


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