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 = {(ab): a ≤ b}, is reflexive and transitive but not symmetric.


ANSWER:

R = {(ab); a ≤ b}
Clearly (aa) ∈ R as 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 (ab), (bc) ∈ R.
Then, 
a ≤ b and b ≤ c
⇒ a ≤ c
⇒ (ac) ∈ R
∴R is transitive.
Hence,R is reflexive and transitive but not symmetric.

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