Q.16 Let A = \{1, 2, 3\}. Then number of relations containing (1, 2) and (1, 3) which are
reflexive and symmetric but not transitive is

(A) 1
(B) 2
(C) 3
(D) 4

Answers (1)

A = \{1, 2, 3\}

The smallest  relations containing (1, 2) and (1, 3) which are
reflexive and symmetric but not transitive is given by 

R = \left \{ (1,1),(2,2),(3,3),(1,2),(1,3),(2,1),(3,1) \right \}

(1,1),(2,2),(3,3) \in R  , so relation R is reflexive.

(1,2),(2,1) \in R    and   (1,3),(3,1) \in R  , so relation R is symmetric.

(2,1),(1,3) \in R  but (2,3) \notin R  , so realation R is not transitive.

Now, if we add any two pairs (2,3)   and (3,2) to relation R, then relation R  will become transitive.

Hence, the total number of the desired relation is one.

Thus, option A is correct.

 

 

 

 

 

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