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
Here, Z + denotes the set of all non – negative integers.
Given that ‘*’ is an operation that is valid in the Positive integers ‘Z + ’ and it is defined as given:
⇒ a*b = a, where a,b∈Z + ,
Since a∈Z + and b∈Z + ,
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*b∈Z + – ...... (1)
It is told from the problem a∈Z + .
The operation ‘*’ defines a binary operation on Z +.