Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let 
be the set of real numbers.
Statement-1 : 
is an integer 
is an equivalence relation on 
.
Statement-2: 
for some rational number 
is an equivalence relation on 
.
Text Solution
Verified by ExpertsThe correct answer is:
A
Now, 
integer and 
integer 
= integer
and 
is transitive
As 
is an integer is true 
is reflexive Also, 
is symmetric
Hence, 
is an equivalence relation but 
is not, as ( 
) is in 
but 
is not in 
.
∴ Statement- 1 is true but Statement- 2 is false.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems