Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this.

On R, defined * by a*b = a + 4b2


Here, Z + denotes the set of all non – negative integers.

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


a*b = a + 4b2, where a,bR,


Since aR and bR,


According to the problem it is given that on applying the operation ‘*’ for two given real numbers it gives a Real number as a result of the operation,


a*bR ...... (1)


Since bR then b2R,


We also know that the sum of two real numbers gives a real number. So,


a + 4b2R ...... (2)


From (1) and (2),


The operation ‘*’ defines a binary operation on R.


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