Determine whether each of the following operations define a binary operation on the given set or not:

Question

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.

Philoid · Accepted Answer

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.

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.

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.