Sets & RelationsmediumFree

Relation on {3,6,9,12}: Reflexive and Transitive Only | JEE

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

Question
Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)}R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\} be a relation on the set A={3,6,9,12}A = \{3, 6, 9, 12\}. The relation is:
AAn equivalence relation
BReflexive and symmetric only
CReflexive and transitive onlycorrect
DReflexive only
Solution
(3,3),(6,6),(9,9),(12,12)∈R⇒R(3, 3), (6, 6), (9, 9), (12, 12) \in R \Rightarrow R is reflexive. (6,12)∈R(6, 12) \in R but (12,6)∉R⇒R(12, 6) \notin R \Rightarrow R is not symmetric. Every chain closes, e.g. (3,6),(6,12)⇒(3,12)∈R⇒R(3, 6), (6, 12) \Rightarrow (3, 12) \in R \Rightarrow R is transitive. ∴R\therefore R is reflexive and transitive only. Correct answer: (3)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Sets & Relations · easy
The relation R = (1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3) on the set A = 1, 2, 3 is:
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…

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