State T for true and F for false.
(i) Let 
be a relation defined on the set 
. Then 
is symmetric, transitive but not reflexive.
(ii) If 
and 
be the set of natural numbers. Then, the mapping 
defined by 
, is onto.
(iii) The relation 
on the set 
defined as 
is reflexive, symmetric and transitive.
(i) (ii) (iii)
Text Solution
Verified by ExpertsC
(i) False
Given that, 
be defined on the set 
.
. Therefore, 
is not reflexive.
. Hence, 
is symmetric.
Since, 
but 
So, 
is not transitive.
(ii) True
Given, 
Since, 
So, 
Range.
Hence, the mapping 
is onto.
(iii) False
Given, 
Since, 
Therefore, 
is not reflexive.
──────────────────────────────────────────────────────────────────────────────────────────
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