Question 4: Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric. Chapter 1 - Relations And Functions

Chapter 1 - Relations And Functions

NCERT Solutions for Class 12 Science Math

Exercise No. 1.1

Question 4:
Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.

ANSWER:

R = {(a, b); a ≤ b}

Clearly (a, a) ∈ R as a = a.

∴R is reflexive.

Now, 

(2, 4) ∈ R (as 2 < 4)

But, (4, 2) ∉ R as 4 is greater than 2. 

∴ R is not symmetric.

Now, let (a, b), (b, c) ∈ R.

Then, 

a ≤ b and b ≤ c

⇒ a ≤ c

⇒ (a, c) ∈ R

∴R is transitive.

Hence,R is reflexive and transitive but not symmetric.