Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive:

a. x R y xy ? 0 x, y R

b. x R y x>y x, y R

c. x R y |x| = |y| x, y R

For each of the above, indicate whether it is an equivalence relation or a partial order. If it is a partial order, indicate whether it is a total order. If it is an equivalence relation, describe its equivalence classes