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  • Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Q. 6 Show that the relation R in the set \{1, 2, 3\}given by R = \{(1, 2), (2, 1)\} is
symmetric but neither reflexive nor transitive.

Answers (1)

best_answer

Let A= \{1, 2, 3\}

R = \{(1, 2), (2, 1)\}

We can see \left ( 1,1 \right ),\left ( 2,2 \right ),\left ( 3,3 \right )\notin R  so it is not reflexive.

As \left ( 1,2 \right )\in R \, and \, \left ( 2,1 \right )\in R so it is symmetric.

(1, 2) \in R \, and\, (2, 1)\in R

But  (1, 1)\notin R so it is not transitive.

Hence, R is symmetric but neither reflexive nor transitive.

 

 

Posted by

seema garhwal

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