Need Solution for R. D.Sharma Maths Class 12 Chapter relations Exercise 1.1 Question 14 sub question 5 Maths Textbook Solution.
Answer:
Hint:
A relation R on set A is
Reflexive relation:
If for every
Symmetric relation:
If is true then is also true for every
Transitive relation:
If
Given:
We have to give the example of a relation which is transitive but neither symmetric nor reflexive.
Solution:
The relation having properties of being transitive but neither symmetric nor reflexive.
Consider a relation R in defined as:
For any we have , since can’t be strictly less than itself.
Infact
∴ Relation is not reflexive.
Now,
But 2 is not less than 1
∴
∴ is not symmetric
Now let
is transitive.