Sets & RelationseasyFree

Relation 2x+y=41 on N: Reflexive, Symmetric, Transitive? | JEE

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

Question
Let RR be a relation on the set NN defined by {(x,y):x,y∈N, 2x+y=41}\{(x, y) : x, y \in N,\ 2x + y = 41\}. Then RR is:
AReflexive
BSymmetric
CTransitive
DNone of thesecorrect
Solution
(1,1):2(1)+1=3≠41⇒R(1, 1): 2(1) + 1 = 3 \ne 41 \Rightarrow R is not reflexive. (1,39)∈R(1, 39) \in R but (39,1):2(39)+1=79≠41⇒R(39, 1): 2(39) + 1 = 79 \ne 41 \Rightarrow R is not symmetric (20,1),(1,39)∈R(20, 1), (1, 39) \in R but (20,39):2(20)+39=79≠41⇒R(20, 39): 2(20) + 39 = 79 \ne 41 \Rightarrow R is not transitive. ∴\therefore none of these. Correct answer: (4)
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