Problem 2

For the problems 5a to 5c, determine whether the relation R on the set of integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ? R if and only if

a) x + y = 0.

b) xy ? 0.

c) x = 1 or y = 1.

d) For the problem 1a, draw a graph illustrating the relation

Problem 1 For each of these subsets in problems 4a to 4e, decide which is the relations on the set {1, 2, 3, 4}, decide whether it is reflexive, symmetric, antisymmetric, and/or transitive. Explain your answer. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} c) {(2, 4), (4, 2), (3, 6)} d) {(2, 2), (2, 3), (3, 2)} e ) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4), (2, -2)} Problem 2 For the problems 5a to 5c, determine whether the relation R on the set of integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) E R if and only if a) x+ y=0. b) xy 20. c) x = 1 ory = 1. d) For the problem 1a, draw a graph illustrating the relation e) for the problem 1b, draw a tabular form to represent the binary relation