Verified Solution • 2025–26 Session moderate

QJEEM24Mabfe0: JEE Main 2024 Mathematics - Class 11 JEEM24Mabfe0 Solution: Let and . Let be a relation on defined by if and only if is an…

Let A={2,3,6,8,9,11}A=\{2,3,6,8,9,11\} and B={1,4,5,10,15}B=\{1,4,5,10,15\} . Let RR be a relation on A×BA \times B defined by (a,b)R(c,d)(a, b) R(c, d) if and only if 3ad−7bc3 a d-7 b c is an even integer. Then the relation RR is

Multiple Choice Options

  • A reflexive but not symmetric.
  • B an equivalence relation.
  • C reflexive and symmetric but not transitive.
  • D transitive but not symmetric.

Step-by-Step Verified Solution

(a,b)R(c,d)⇒3ad−7bc∈(a, b) R(c, d) \Rightarrow 3 a d-7 b c \in even

For reflexive

(a,b)R(a,b)⇒3ab−7ba=−4ab∈(a, b) R(a, b) \Rightarrow 3 a b-7 b a=-4 a b \in even

For symmetric

(a,b)R(c,d)(a, b) R(c, d)

JEE Main 2024 (Online) 8th April Evening Shift Mathematics - Sets and Relations Question 15 English Explanation

then

(c,d)R(a,b)=3bc−7ad(c, d) R(a, b)=3 b c-7 a d

∈\in even

Now check for transitive

amp;(a,b)R(c,d) and (c,d)R(e,f) then (a,b)R(e,f)3ad−7bc=2m⇒(2,5)R(6,8) and 3cf−7ed=2n(6,8)R(9,4) then 3af−7eb≠ even ∉(2,5)R(9,4)⇒ Not transitive option (3)\begin{aligned}& \begin{array}{ll}(a, b) R(c, d) \text { and }(c, d) R(e, f) \text { then }(a, b) R(e, f) \\3 a d-7 b c=2 m \quad \Rightarrow (2,5) R(6,8) \text { and } \\3 c f-7 e d=2 n \quad (6,8) R(9,4) \\\text { then } 3 a f-7 e b \neq \text { even } \notin(2,5) R(9,4) \\\Rightarrow \text { Not transitive option }(3)\end{array}\end{aligned}

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