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QJEEM24Ma563f: JEE Main 2024 Mathematics - Class 11 JEEM24Ma563f Solution: Let and be a relation on . Let be the equivalence relation on…

Let A={1,2,3,4}A=\{1,2,3,4\} and R={(1,2),(2,3),(1,4)}R=\{(1,2),(2,3),(1,4)\} be a relation on A\mathrm{A} . Let S\mathrm{S} be the equivalence relation on A\mathrm{A} such that R⊂SR \subset S and the number of elements in S\mathrm{S} is n\mathrm{n} . Then, the minimum value of nn is __________.

Step-by-Step Verified Solution

amp;A={1,2,3,4}amp;R={(1,2),(2,3),(1,4)}\begin{aligned}& A=\{1,2,3,4\} \\\\& R=\{(1,2),(2,3),(1,4)\}\end{aligned}

SS is equivalence for R < S and reflexive

{(1,1),(2,2),(3,3),(4,4)}\{(1,1),(2,2),(3,3),(4,4)\}

for symmetric

{(2,1),(4,1),(3,2)}\{(2,1),(4,1),(3,2)\}

for transitive

{(1,3),(3,1),(4,2),(2,4)}\{(1,3),(3,1),(4,2),(2,4)\}

Now set S={(1,1),(2,2),(3,3),(4,4),(1,2)S=\{(1,1),(2,2),(3,3),(4,4),(1,2) , (2,3),(1,4),(4,3),(3,4),(2,1),(4,1),(3,2),(1,3),(3(2, 3),(1,4),(4,3),(3,4),(2,1),(4,1),(3,2),(1,3),(3 , 1), (4,2),(2,4)}(4,2),(2,4)\}

n(S)=16n(S)=16

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