1. Let R be a relation on Z defined by Ry if and only if x + y is even. Is R reflexive? Is R symmetric? Is R transitive? Prove or give a counterexample for each. Note: For transitivity, you may rely on the even/oddness of the sum of two odd numbers, the dif- ference of an even number and an odd number, the product of two even numbers, etc. without proving it. It is possible to use a direct line of proof- if you do you will get bonus points, but make sure not to spend too much time on it!

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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1. Let R be a relation on Z defined by Ry if and only if x +y is even. Is R reflexive? Is R symmetric? Is
R transitive? Prove or give a counterexample for each.
Note: For transitivity, you may rely on the even/oddness of the sum of two odd numbers, the dif-
ference of an even number and an odd number, the product of two even numbers, etc. without proving
it. It is possible to use a direct line of proof- if you do you will get bonus points, but make sure not to
spend too much time on it!
Transcribed Image Text:1. Let R be a relation on Z defined by Ry if and only if x +y is even. Is R reflexive? Is R symmetric? Is R transitive? Prove or give a counterexample for each. Note: For transitivity, you may rely on the even/oddness of the sum of two odd numbers, the dif- ference of an even number and an odd number, the product of two even numbers, etc. without proving it. It is possible to use a direct line of proof- if you do you will get bonus points, but make sure not to spend too much time on it!
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