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JEE Main 202522 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 22 January · Evening Shift · Mathematics · Sets and Relations

Let A=\ 1,2,3\ . The number of relations on A , containing (1,2)...

Let A={1,2,3}A=\{1,2,3\}. The number of relations on AA, containing (1,2)(1,2) and (2,3)(2,3), which are reflexive and transitive but not symmetric, is ______ -

Correct answer

0

Step-by-step solution

RR is reflexive ⇒R\Rightarrow R have (1,1),(2,2),(3,3)R(1,1),(2,2),(3,3) R is transitive ∵(1,2),(23)∈R∴(1,3)∈R∴R1={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\begin{aligned} & \because(1,2),(23) \in R \quad \therefore(1,3) \in R \\ & \therefore \quad R_1=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\} \end{aligned} Clearly R1R_1 is reflexive and transitive but not symmetric. Similarly, R2={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,2)}R3={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(2,1)}\begin{aligned} & R_2=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,2)\} \\ & R_3=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(2,1)\} \end{aligned} Therefore, 3 relations are possible
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