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Question -

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 it reflexive and transitive.



Answer -

A relation R in A is said to be reflexive if aRa for all a∈A
 
R is said to be transitive if aRb and bRc ⇒ aRc
for all a, b, c ∈ A.
Hence for R to be reflexive (b, b) and (c, c) must be there in the set R.
Also for R to be transitive (a, c) must be in R because (a, b) ∈ R and (b, c) ∈ R so (a, c) must be in R.
So at least 3 ordered pairs must be added for R to be reflexive and transitive.

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