The relation R is on the set of all integers, where (x,y) is an element of R if and only if x is a multiple of y.
Would this relation be reflexive, symmetric, antisymmetric, and/or transitive?
I have determined it to be reflexive, antisymmetric, and transitive... Apparently my textbook tells me that it is NOT antisymmetric. Yet I would think it would be because "x is a multiple of y" should mean that if (x,y) is an element and (y,x) is an element then x=y, because x can be simply (1*y).
Hint: $3$ is a multiple of $-3$, and $-3$ is a multiple of $3$.