Let R1 and R2 be relations on a set A = {1, 2, 3, 4}.In particular, let R, = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)} andR2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (4, 1), (4, 2)}.Determine the following:a) Whether or not R¡ is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not.b) Whether or not R2 is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not.c) The relation R, ° R2.d) The relation R2 ° Rị.e) R1 U R2f) R1 n R2g) The reflexive, symmetric and transitive closures of both R¡ and R2.

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Let R, and R2 be relations on a set A = {1, 2, 3, 4}. In particular, let R, = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)} and R2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (4, 1), (4, 2)}. Determine the following: a) Whether or not R, is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not. b) Whether or not R, is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not. c) The relation R1 ° R2. d) The relation R, ° R1. e) R1 U R2 f) R1 n R2 g) The reflexive, symmetric and transitive closures of both R¡ and R2.

Let R, and R2 be relations on a set A = {1, 2, 3, 4}. In particular, let R, = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)} and R2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (4, 1), (4, 2)}. Determine the following: a) Whether or not R, is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not. b) Whether or not R, is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not. c) The relation R1 ° R2. d) The relation R, ° R1. e) R1 U R2 f) R1 n R2 g) The reflexive, symmetric and transitive closures of both R¡ and R2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let R1 and R2 be relations on a set A = {1, 2, 3, 4}.
In particular, let R, = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4, 3) (4, 4)} and
R2 = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (4, 1), (4, 2)}.
Determine the following:
a) Whether or not R¡ is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not.
b) Whether or not R2 is reflexive, irreflexive, symmetric, anti-symmetric and transitive or not.
c) The relation R, ° R2.
d) The relation R2 ° Rị.
e) R1 U R2
f) R1 n R2
g) The reflexive, symmetric and transitive closures of both R¡ and R2.

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