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show that the relation R in the set {1,2,3} givwn by R = {(1,2) (2,1)} is symmetic but neither reflexive nor tresitive.

show that the relation R in the set {1,2,3} givwn by R = {(1,2)
(2,1)} is symmetic but neither reflexive nor tresitive.

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
"Reflexive" means that (a, a) is included for every element a in A.
"Symmetric" means that if (a, b) is included, then (b, a) is also included.
"Transitive" means that if (a, b) and (b, c) are included, then (a, c) is also included
In the above given relation R{1,2,3} givwn by R = {(1,2) (2,1)}
If (a, b) is included, then (b, a) is also included
Hence it is only symmetric but not transitive and reflexive
Thanks and Regards
Shaik Aasif
askIITians faculty

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