Q. 153.5( 2 Votes )

Given the relatio

Answer :

Given is:

R = {(1, 2), (2, 3)} on the set A.


A = {1, 2, 3}


Right now, we have


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


Symmetric Relation:


We know (1, 2) R


Then, (2, 1) R


Also, (2, 3) R


Then, (3, 2) R


So, add (2, 1) and (3, 2) in R, so that we get


R’ = {(1, 2), (2, 1), (2, 3), (3, 2)}


Transitive Relation:


We need to make the relation R’ transitive.


So, we know (1, 2) R and (2, 1) R


Then, (1, 1) R


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


Then, (2, 2) R


Also, (2, 1) R and (1, 2) R


Then, (2, 2) R


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


Then, (3, 3) R


Add (1, 1), (2, 2) and (3, 3) in R’, we get


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


Thus, we have got a relation which is reflexive, symmetric and transitive.


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


The ordered pair added are (1, 1), (2, 2), (3, 3), (3, 2).


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