Since 1 + 1 6= 0, this relation is not reflexive. Since
x + y = y + x, it follows that x + y = 0 if and only if y + x = 0,
so the relation is symmetric. Since (1, −1) and (−1, 1) are both in R,
the relation is not antisymmetric. The relation is not transitive; for
example, (1, −1) ∈ R and (−1, 1) ∈ R, but (1, 1) 6∈ R.
