1. Determine whether the following relations \( R \) on the set of all integers are reflexive, symmetric, antisymmetric, transitive, asymmetric, and/or irreflexive.
(a) \( R_{1}=\{(x, y): x+y=0\} \)
(b) \( R_{2}=\{(x, y): x= \pm y\} \)
(c) \( R_{3}=\{(x, y): x=y+1 \) or \( x=y-1\} \)
(d) \( R_{4}=\{(x, y): x=1\} \)
(e) \( R_{5}=\{(x, y): x \) and \( y \) are both negative or both nonnegative \( \} \)