Q. 35.0( 2 Votes )

Mark the tick aga

Answer :

Given set A = {1, 2, 3}


And R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}


Formula


For a relation R in set A


Reflexive


The relation is reflexive if (a , a) R for every a A


Symmetric


The relation is Symmetric if (a , b) R , then (b , a) R


Transitive


Relation is Transitive if (a , b) R & (b , c) R , then (a , c) R


Equivalence


If the relation is reflexive , symmetric and transitive , it is an equivalence relation.


Check for reflexive


Since , (1,1) R , (2,2) R , (3,3) R


Therefore , R is reflexive ……. (1)


Check for symmetric


Since , (1,2) R and (2,1) R


(2,3) R and (3,2) R


Therefore , R is symmetric ……. (2)


Check for transitive


Here , (1,2) R and (2,3) R but (1,3) R


Therefore , R is not transitive ……. (3)


Now , according to the equations (1) , (2) , (3)


Correct option will be (A)

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