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1. (15 points) For each of the following binary relations R on N, determine which of the given ordered pairs belong to R. Select all that apply. Let N denotes the set of non-negative integers. Use this definition for the entirety of this homework. (a) (5 points) zRy 81 O (1,11) O ( O ( O ( O ( 2. (8 points) Identify each relation on N as one-to-one, one-to-many, many-to-one, or many-to-many. (a) (2 points) R = {(1, 2), (2, 1), (5, 7), (1, 3), (4, 8) } O one-to-one one-to-many OO many-to-one O many-to-many (b) (2 points) R = {(2, 8), (1, 3), (2, 1), (4, 8), (5, 2) } one-to-one one-to-many many-to-one many-to-many (c) (2 points) R = {(1, 13), (3, 8), (2, 13), (5, 21), (10, 69) } O one-to-one one-to-many OOO many-to-one many-to-many (d) (2 points) R = {(5, 1), (10, 5), (6, 2), (8, 3), (7, 4) } O one-to-one one-to-many many-to-one O many-to-many 3. (15 points) Determine whether the following relations are reflexive, symmetric, antisymmetric and /or transitive. Select all that apply. (a) (5 points) Let S = all Mines students and aRb a is older than b. O Reflexive O Symmetric Antisymmetric O Transitive (b) (5 points) Let S = Z and xRy 4 x - y z xy O Reflexive O Symmetric Antisymmetric O Transitive (c) (5 points) Let S = Z and xRy x = ky for some integer k. O Reflexive O Symmetric Antisymmetric O Transitive