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

Answers (1)

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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