Consider a relation $\displaystyle R$ defined on the integers. Determine for the following if the relations are reflexive, symmetric, antisymmetric, transitive, partial orders, equivalence relations.

a) $\displaystyle R=\{(a,b)|a^2\geq b\}$

b) $\displaystyle R=\{(a,b)|a=|b|\}$

c) $\displaystyle R=\{(a,b)|5a=2b\}$

d) $\displaystyle R=\{(a,b)|ab\leq0\}$