Determine whether each of the binary relation R defined on the given sets A is reflexive, symmetric, antisymmetric, or transitive. If a relation has a certain property, prove this is so; otherwise provide a counterexample to show that it does not. (a) A = Z: (a, b) E R if and only if ab > 0. (b) A = R: (a, b) R if and only if a^2=b^2 (c) A = N: (a, be R if and only if a/b is an integer.