This is a question from book "Discrete Mathematics and Its Applications".
Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where(x, y) ∈ R if and only if
b) $xy \ge 1.$
The answer provided by the book is: $R$ is symmetric and transitive.
Why isn't $R$ reflexive?
I think $R$ is reflexive because $x$ and $y$ are integers, since $xy \ge 1$, they are positive integers or negative integers, that $xx \ge 1$ should be true, that $R$ should be reflexive.