Answer :

A relation R on a set A is said to be reflexive if every element of A is related to itself.


Thus, R is reflexive, iff (a, a) R, for every a A


We have,


A = {a, b, c} and R = {(a, a), (b, c), (a, b)}


Therefore by definition of reflexive relation, if a, b, c A then (a, a),(b, b) and (c, c) R.


We observe that since (b, b) and (c, c) does not belong to R so R is not reflexive. We need to add (b, b) and (c, c) in R in order to make it reflexive.


A relation R on a set A is said to be transitive iff aRb and bRc then aRc for all a,b,c A


i.e., (a, b) R and (b, c) R


(a, c) R for all a,b,c A


We observe that since (a, c) does not belong to R so R is not transitive. We need to add (a, c) in R in order to make it transitive.


Hence, minimum number of ordered pairs to be added in R to make R reflexive and transitive are (b, b), (c, c) and (a, c).


Now, R = {(a, a), (b, b), (c, c), (a, c), (b, c), (a, b)} is Reflexive and Transitive.


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