Please solve RD Sharma maths Class 12 Chapter Relations Exercise 1.1 Question 1 Sub question (i) maths text book solution.
Answer : Reflexive, symmetric, transitive.
Hint :
If is reflexive
If is symmetric
If is transitive
Given :
Solution : A relation on set A is said to be reflexive if every element of A is related to itself.
Thus, is reflexive
A relation on set A is said to be symmetric relation if
for all
i.e.
A relation on set A is said to be transitive relation
If
i.e and
for all
Now, let's get back to the actual problem
For Reflexive :
and
work at same place
Similarly, and
work at the same place.
So, is reflexive.
For Symmetric :
It is given that and
work at the same place.
So, we can say that and
work at the same place.
So, is symmetric.
For Transitive:
Let be a person such that
and
work at the same place.
And we know that and
work at the same place.
So, we can say that and
work at the same place.
So, is Transitive.