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JEE Main 20257 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Sets and Relations

The number of relations on the set A=\ 1,2,3\ containing at most 6...

The number of relations on the set A={1,2,3}\mathrm{A}=\{1,2,3\} containing at most 6 elements including (1,2)(1,2), which are reflexive and transitive but not symmetric, is ________

Correct answer

0

Step-by-step solution

<br/>A={1,2,3}(1,1),(2,2),(3,3),(1,2)∈R<br/>\begin{aligned}<br/>& A=\{1,2,3\} \\ & (1,1),(2,2),(3,3),(1,2) \in R<br/>\end{aligned}
Remaining elements are
(2,1),(2,3),(1,3),(3,1),(3,2)(2,1),(2,3),(1,3),(3,1),(3,2)
(1) If relation contains exactly 4 elements = 1 way
(2) if relation contains exactly 5 elements
It can be (1,3),(3,2)⇒2(1,3),(3,2) \Rightarrow 2 ways
(3) If relation contain exactly 6 elements
It can be ((2,3),(1,3)),((1,3),(3,2)),((3,1),(3,2))((2,3),(1,3)),((1,3),(3,2)),((3,1),(3,2))
⇒3\Rightarrow 3 ways.
Total =6=6 ways
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