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

Answers (1)

Answer:

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

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

Solution:

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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