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

Question

Philoid · Accepted Answer

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

⇒ a*b = ab, 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)

We know that p q>0 if p>0 and q>0.

⇒ ab>0∈N

⇒ ab∈Z ⁺

∴ The operation * defines a binary operation on Z ⁺.

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

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 = ab

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