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Explain solution for RD Sharma Class 12 Chapter Relation Exercise 1.1 Question 17 Maths textbook solution.

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At least 3 ordered pairs must be added for R to be reflexive and transitive


A relation R on set A is

Reflexive relation:

If  (a, a) \in R for every a \in A

Symmetric relation:

If (a,b) is true then (b,a)  is also true for every a, b \in A

Transitive relation:

If  (a,b) and (b, c) \in R, then (a, c) \in R   for every a, b, c \in A

Given:  Minimum number of order pair that makes R reflexive and transitive.


A relation R in A is said to be reflexive if aRa for all a \in A

R is said to be transitive if aRb and bRc then aRc for all a, b, c \in A

Hence for R to be reflexive (b,b) and (c,c)must be there in set R

Also for R to be transitive (a,c) must be in R because (a, b) \in R(b, c) \in 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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