Q. 2 A5.0( 2 Votes )

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 Z + , defined * by a*b = a – b

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

Answer :

Given that ‘*’ is an operation that is valid in the Positive integers ‘Z + ’ and it is defined as given:


a*b = a – b, where a,bZ +


Since aZ + and bZ + ,


According to the problem it is given that on applying the operation ‘*’ for two given positive integers it gives a positive integer as a result of the operation,


a*bZ + ...... (1)


Let us take the values a = 1 and b = 2


a – b = 1 – 2


a – b = – 1Z +


The operation * does not define a binary operation on Z +


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