Chapter 1 - Relations And Functions

NCERT Solutions for Class 12 Science Math

Exercise No. 1.1

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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.