Let A = {a, b, c} and the relation R be defined on A as follows:

R = {(a, a), (b, c), (a, b)}.

Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive.

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.