1.Let R be the "greater than" relation on the set of integers, formally defined as follows: for all x, y Z, x R y x > y. Please show your work to determine whether or not the given relation is: (a) (2 points) Reflexive: (b) (2 points) Symmetric: (c) (2 points) Anti-symmetric: (d) (2 points) Transitive:

2.Let A be a Cartesian product ZZ, and let F be a relation defined on A as follows: For all (x1, y1) and (x2, y2) A : (x1, y1) F (x2, y2) x1 = x2 Please show your work to determine whether or not the given relation is: (a) (2 points) Reflexive: (b) (2 points) Symmetric: (c) (2 points) Anti-symmetric: (d) (2 points) Transitive:

3.Represent each of these relations on the set {0, 3, 7}with a matrix, such that the elements of the given set are listed in an increasing order: Use matrix representation of a relation to determine whether the following relations are reflexive and symmetric. 1){(0, 3), (0, 7), (3, 7), (7, 7)} (a) (2 points) Matrix representation? (b) (2 points) Reflexive? (c) (2 points) Symmetric?

2){(0, 0), (3, 3), (7, 7)} (a) (2 points) Matrix representation? (b) (2 points) Reflexive?

(c) (2 points) Symmetric?