Let # represent one of the four basic arithmetic operations such that, for any nonzero real numbers r and s,
r # 0 = r and r # s = s # r
Which arithmetic operation(s) does the symbol # represent?
A. + only
B. X only
C. - only
D. - and X
E. + and divide
If r # 0 = r, then the symbol # can represent either addition or subtraction, but not multiplication or division. Since it is also given that r # s = s # r, the operation # is commutative. Since addition is commutative and subtraction is not commutative, the symbol # represents only addition.