Given the relation R={(1,2)(2,3)} on set A={1,2,3} add a minimum number of order pair so that enlarged relation is symmetric ,transitive an d reflexive.

a relation on set A={1,2,3} is reflexive if for every element xA ,xRx
if R is reflexive relation , missing ordered pair are  {(1,1),(2,2),(3,3)} .
if we add these , the obtain new relation is R={(1,2),(2,3),(1,1),(2,2),(3,3)}

a relation is symmetric if for every a,bA ,aRbbRa
therefore following ordered pair are required to make the relation symmetric:(2,1),(3,2)
if we add these, the obtain new relation is R={(1,2),(2,3),(2,1),(3,2)}

a relation is transitive if for every a,b,cA, (aRb &bRc aRc
so for making it transitive we must add {(1,3)}
the obtain new relation is {(1,2),(2,3),(1,3)}

now if the relation is symmetric , transitive and reflexive;
then new relation R={(1,1),(2,2),(3,3),(1,2),(2,1)(2,3),(3,2),(1,3),(3,1)}

hope this helps you

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