Sets & RelationseasyFree

Reflexive but Not Symmetric Relation on {1,2,3} | JEE

JEE Maths question with a full step-by-step solution.

Question
The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\} on the set A={1,2,3}A = \{1, 2, 3\} is:
AReflexive but not symmetriccorrect
BReflexive but not transitive
CSymmetric and transitive
DNeither symmetric nor transitive
Solution
(1,1),(2,2),(3,3)∈R⇒R(1, 1), (2, 2), (3, 3) \in R \Rightarrow R is reflexive. (1,2)∈R(1, 2) \in R but (2,1)∉R⇒R(2, 1) \notin R \Rightarrow R is not symmetric. (1,2),(2,3)∈R⇒(1,3)∈R(1, 2), (2, 3) \in R \Rightarrow (1, 3) \in R, so the chain closes ⇒R\Rightarrow R is transitive. ∴R\therefore R is reflexive but not symmetric. Correct answer: (1)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Sets & Relations · easy
The relation R is defined in A = 1, 2, 3 by aRb if |a² - b²| ≤ 5 . Which of the following…
Sets & Relations · medium
The relation R defined on the set A = 1, 2, 3, 4, 5 by R = (x, y) : |x² - y²| < 16 is giv…
Sets & Relations · easy
If A is the set of even natural numbers less than 8 and B is the set of prime numbers les…
Sets & Relations · easy
The relation R is defined on the set of natural numbers as (a, b) : a = 2b . Then R^(-1)…

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath