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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)
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