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  • Please Solve R. D. Sharma class 12 Chapter relations Exercise 1.1 Question 11 Maths textbook Solution.

Please Solve R. D. Sharma class 12 Chapter relations Exercise 1.1 Question 11  Maths textbook Solution.
 

Answers (1)

Answer:

 No, it is not true that every relation which is symmetric and transitive is also reflexive.

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

Given:

Answer that, whether every relation which is symmetric and transitive is also reflexive.

Solution:

No, it is not necessary that a relation that is symmetric and transitive is reflexive as well.

For example:

R=\{(1,1),(1,2),(2,1)\} \text { on } A=\{1,2\} is symmetric and transitive but not reflexive.

Because (2,2) \notin R

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