Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where N is the set of all natural numbers. Prove or disprove reflexivity, symmetry and transitivity of R

Consider the relation R on R given by R = {(a, b) | a−b > 3 or a−b = 0}. (a) Show that R is not an equivalence relation. (b) Determine whether R is or is not a partial order. (You must support your answer.)

Which of the following relations on R are equivalence relations?

Let R3 be the relation on Z+ such that xR3y if and only if 2x – 3y > 0. (Recall that Z+ = {1,2,3, 4, ...}, the positive integers.) 14) Prove or Disprove: R3 is anti-symmetric.