Which relations are irreflexive?
a) x + y = 0.
b) x = ±y.
c) x − y is a rational number.
d) x = 2y.
e) xy ≥ 0.
f ) xy = 0.
g) x = 1.
h) x = 1 or y = 1.
If a set is irreflexive when no element in a set is related to itself then doesn't that mean none of the above sets are irreflexive since (0,0) or (1,1) exists in all of them.
This depends on what set your relation is defined on. If for example the relations are defined on the positive integers, then relation f) is irreflexive, as there exists no positive integer $n$ such that $nn = 0$. However, assuming that all these relations are over the natural numbers including zero, then it is correct that none of the above are irreflexive.