Question

Any function with domain R×R is a binary operation​ .true or false .give reason

Answer 1

True, Any function with domain RxR is a binary operation.

• The binary operations * on a non-empty set A are functions from AxA to A. The binary operation *:AxA->A.
• It is an operation of two elements of the set whose domain and co-domains are in the same set.
• Properties of binary operation are Closure and Addition are the binary operations on each sets of natural numbers(N), Integer(Z), Rational numbers(Q), complex numbers(C), Real numbers(R).

Answer 2

Answer:

Step-by-step explanation:

We are initially given a valid function with domain R×R and an unknown co-domain. A binary operation on R defines a function from R×R to R. While the domain of the given (valid) function is specified to be R×R, the domain is not explicitly specified to be R. Hence, generally, this statement is false, as in: for the binary operation a∗b=+sqrt(a+b)would result in C for, say a=−1,b=−2