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Explain solution for RD Sharma Class 12 Chapter Relation Exercise 1.1 Question 16 Maths textbook solution.

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Answer:

only 1 ordered pair maybe added to R so that it may become a transitive relation on A

Hint:

 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 : A=\{1,2,3\}

Solution :

  R=\{(1,2),(1,1),(2,3)\} be a relation on A

To make R transitive we shall add (1,3) only  R^{\prime}=\{(1,2),(1,1),(2,3),(1,3)\}

As we know,

Transitive relation

\\\text {x=y} \; and \; \text {y=z}\\ \text {Then} \; \text {x=z}

 

Note: for R to be transitive (a,c) must be in R because  (a, b) \in R \text { and }(b, c) \in R  So, (a,c) must be in R

 

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