let S be the set of people in the United States Test the fol

let S be the set of people in the United States. Test the following binary relations on S for relexivity, symmetry, antisymmetry, and transitivity.

Solution

a)antisymmetric, transitive. If x is the husband of y then y is assumed to be a woman, so we never have x y and y x except when x = y
b)symmetric
c)reflexive, symmetric, transitive
d)none. not symmetric because y could be the sister of x