Question 18 (a-d): Test the following binary relations on the given sets S for reflexivity, symmetry, antisymmetry, and transitivity.

cs-set ofall finite-length binary strings xpy ++ x is a prefix ofy d. S set of all finite-length binary strings xpy++x has the same number of Is asy 18. Test the following binary relations on the given sets S for reflexivity, symmetry, antisymmetrn, . transitivity spy, x = ky for some integer k xpy there is a prime number p such that plx and ply c. S , 2, 3, 4, 5, 6, 7, 8, 9)) d.s-p(1,2, 3, 4, 5, 6, 7, 8, 9) 19. Let S be the set of people in the United States. Test the following binary relations on S for reflexivity. metry, antisymmetry, and transitivity. a. xpy +x is at least as tall as y. bxpy x is taller than y. c. xpy x is the same height as y