Problem 1.. Either provide complete proof of each listed below statement or show that the statement is not true (by counterexample). (a) If R and S are two symmetric relations on a set A then their R NS and RUS are symmetric relations on A. Solution. (b) If R and S are two transitive relations on a set A then their RU S is transitive relation on A. What about RNS ?.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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please solve this abstract algebra question for me 

Problem 1.. Either provide complete proof of each listed below statement or show that the
statement is not true (by counterexample).
(a) If R and S are two symmetric relations on a set A then their R NS and RUS are
symmetric relations on A.
Solution.
(b) If R and S are two transitive relations on a set A then their RU S is transitive relation
on A. What about RNS ?.
Transcribed Image Text:Problem 1.. Either provide complete proof of each listed below statement or show that the statement is not true (by counterexample). (a) If R and S are two symmetric relations on a set A then their R NS and RUS are symmetric relations on A. Solution. (b) If R and S are two transitive relations on a set A then their RU S is transitive relation on A. What about RNS ?.
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