Which of the Following is a Binary Operation if a and b are in S?

Question

Which of the Following is a Binary Operation if a and b are in S?

a. a*b = ab + b², S = set of negative numbers

b a*b = square root of a+b ; S = set of positive numbers

c a*b = ab-a; S = set of real numbers except zero

d a*b = a² - b²; S = set of real numbers except zero

I have answered B but I am not sure of it.

Answer 1

Answer is C

a is a real number that is not 0

b is a real number that is not 0

ab = real number that is not zero

ab - a = real number that is not zero as |ab| not = |a|

The answer is not B because here, set of positive numbers here probably means set of positive integer numbers.