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Let R and S be two relations both on A. Show that (a) If R and S are both reflexive, is RnS also reflexive? (b) If R and S are both symmetric, is RnS also symmetrie? (c) If R and S are both transitive, is RnS also transitive?

Let R and S be two relations both on A. Show that (a) If R and S are both reflexive, is RnS also reflexive? (b) If R and S are both symmetric, is RnS also symmetrie? (c) If R and S are both transitive, is RnS also transitive?

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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Let R and S be two relations both on A. Show that
(a) If R and S are both re exive, is R \ S also re exive?
(b) If R and S are both symmetric, is R \ S also symmetric?
(c) If R and S are both transitive, is R \ S also transitive?
Note: Of course, yes or no answers are not acceptable. Show your work brie y.

Let R and S be two relations both on A. Show that (a) If R and S are both reflexive, is RnS also reflexive? (b) If R and S are both symmetric, is RnS also symmetric? (c) If R and S are both transitive, is RnS also transitive? Note: Of course, yes or no answers are not acceptable. Show your work briefly.
Transcribed Image Text:Let R and S be two relations both on A. Show that (a) If R and S are both reflexive, is RnS also reflexive? (b) If R and S are both symmetric, is RnS also symmetric? (c) If R and S are both transitive, is RnS also transitive? Note: Of course, yes or no answers are not acceptable. Show your work briefly.
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