The relation R on Z is defined by (x,y) in R if and only if x-y is even. Write as a set by listing its elements.
The confuses me. Is the question asking which elements of the given set are in R? Then that would be .
order doesn't matter in listing set elements. it DOES matter in listing ordered pairs (note the "ordered" in ordered pair).
the ordered pair (a,b) is not, in general, the same pair as (b,a).
for example, if R is the relation <, then (3,4) is in R, but (4,3) is NOT.