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1. Suppose R = {(1,1), (1, 4), (2, 1), (2, 2), (3, 2), (3, 3), (3, 4), (4, 1), (4,2), (4, 4)} be a relation from A = {1, 2, 3, 4} to itself. You must show that the property holds or give a counterexample a) Is R reflexive, irreflexive, or neither? c) Is R transitive? b) Is R symmetric, antisymmetric, or neither? d) Draw a graph of R.

1. Suppose R = {(1,1), (1, 4), (2, 1), (2, 2), (3, 2), (3, 3), (3, 4), (4, 1), (4,2), (4, 4)} be a relation from A = {1, 2, 3, 4} to itself. You must show that the property holds or give a counterexample a) Is R reflexive, irreflexive, or neither? c) Is R transitive? b) Is R symmetric, antisymmetric, or neither? d) Draw a graph of R.

Advanced Engineering Mathematics
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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1. Suppose R= You must show that the property holds or give a counterexample {(1,1), (1, 4), (2, 1), (2, 2), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2). (4, 4)} be a relation from A = {1,2, 3, 4} to itself. a) Is R reflexive, irreflexive, or neither? c) Is R transitive? b) Is R symmetric, antisymmetric, or neither? d) Draw a graph of R.
Transcribed Image Text:1. Suppose R= You must show that the property holds or give a counterexample {(1,1), (1, 4), (2, 1), (2, 2), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2). (4, 4)} be a relation from A = {1,2, 3, 4} to itself. a) Is R reflexive, irreflexive, or neither? c) Is R transitive? b) Is R symmetric, antisymmetric, or neither? d) Draw a graph of R.
2. Let A = {0, 1, 2, 3, 4, 5, 6, 7,8, 9} and suppose R is a relation defined by a is related to b if a divides b. You must show that the property holds or give a counterexample. a) Write out the ordered pairs that make up the set R. b) Is R reflexive, irreflexive, or neither? d) Is R transitive? c) Is R symmetric, antisymmetric, or neither? e) Draw a graph of R.
Transcribed Image Text:2. Let A = {0, 1, 2, 3, 4, 5, 6, 7,8, 9} and suppose R is a relation defined by a is related to b if a divides b. You must show that the property holds or give a counterexample. a) Write out the ordered pairs that make up the set R. b) Is R reflexive, irreflexive, or neither? d) Is R transitive? c) Is R symmetric, antisymmetric, or neither? e) Draw a graph of R.
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