Determine whether or not each definition * given below gives a binary

1.	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 = ab2Here, Z+ denotes the set of all non – negative integers.
Answer» Given that ‘’ is an operation that is valid in the Real Numbers ‘R’ and it is defined as given: ⇒ ab = ab², where a,b∈R Since a∈R and b∈R, 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, ⇒ ab∈R ...... (1) We know that ab∈R if a∈R and b∈R *∴ The operation defines a binary operation on R.**

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 = ab2Here, Z+ denotes the set of all non – negative integers.

Answer»

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

⇒ a*b = ab², where a,b∈R

Since a∈R and b∈R,

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*b∈R ...... (1)

We know that ab∈R if a∈R and b∈R

∴ The operation * defines a binary operation on R.

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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 = ab2Here, Z+ denotes the set of all non – negative integers.

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