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JEE Main 20258 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
8 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 8 April · Evening Shift · Mathematics · Sets and Relations

Let A=\ 0,1,2,3,4,5\ . Let R be a relation on A defined by (x, y) ∈...

Let A={0,1,2,3,4,5}A=\{0,1,2,3,4,5\}. Let RR be a relation on A defined by (x,y)∈R(x, y) \in R if and only if max {x,y}∈{3,4}\{x, y\} \in\{3,4\}. Then among the statements \left(\mathrm{S}_1\right):ThenumberofelementsinRis18,and(S2): The number of elements in R is 18 , and \left(\mathrm{S}_2\right) : The relation R is symmetric but neither reflexive nor transitive

Options

  1. Aboth are true
  2. Bboth are false
  3. Conly (S2)\left(\mathrm{S}_2\right) is true
  4. Donly (S1)\left(\mathrm{S}_1\right) is true

Correct answer

C. only (S2)\left(\mathrm{S}_2\right) is true

Step-by-step solution

A={0,1,2,3,4,5}A=\{0,1,2,3,4,5\}
R≡{(0,3),(3,0),(0,4),(4,0),(1,3),(3,1),(1,4)\mathrm{R} \equiv\{(0,3),(3,0),(0,4),(4,0),(1,3),(3,1),(1,4),
(4,1),(2,3),(3,2),(2,4),(4,2),(3,3),(3,4),(4,3)(4,1),(2,3),(3,2),(2,4),(4,2),(3,3),(3,4),(4,3),
(4,4)}(4,4)\}
Total 16 elements
Not reflexive as (0,0),……,(2,2)∉R(0,0), \ldots \ldots,(2,2) \notin \mathrm{R}
Symmetric ∵∀\because \forall all a,b
(a,b)&(b,a)∈R(a, b) \&(b, a) \in R
Not transitive ∵(0,3),(3,1)∈R\because(0,3),(3,1) \in R
but (0,1)∉R(0,1) \notin \mathrm{R}
⇒\Rightarrow Only S2\mathrm{S}_2 correct
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