Determine which of the three properties (reflexive, symmetric, and transitive) apply to each relation.
(a) Let R be the relation on N given by x R y iff x divides y.
(b) Let X be a set and let R be the relation “⊆” defined on subsets of X.
(c) Let S be the set of people in the school. Define R on S by x R y iff “x likes y.”
(d) Let R be the relation {(1, 1), (1, 2), (2, 2), (1, 3), (3, 3)} on the set {1, 2, 3}.
(e) Let R be the relation on R given by x R y iff x – y is rational.
(f ) Let R be the relation on R given by x R y iff x – y is irrational.
(g) Let R be the relation on R given by x R y iff (x – y)2
(h) Let R be the relation on R given by x R y iff | x − y | ≤ 2.