Verified Solution • 2025–26 Session moderate

QJEEM23Maf7dc: JEE Main 2023 Mathematics - Class 11 JEEM23Maf7dc Solution: The minimum number of elements that must be added to the…

The minimum number of elements that must be added to the relation R={(a,b),(b,c)}\mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\} on the set {a,b,c}\{a, b, c\} so that it becomes symmetric and transitive is :

Multiple Choice Options

  • A 7
  • B 3
  • C 4
  • D 5

Step-by-Step Verified Solution

For symmetric (b,a),(c,b)∈R(b,a),(c,b)\in R

For transitive (a,c)∈R(a,c)\in R

⇒(c,a)∈R\Rightarrow (c,a)\in R

∴(a,b),(b,a)∈R\therefore (a,b),(b,a)\in R

⇒(a,a)∈R\Rightarrow (a,a)\in R

(b,c),(c,b)∈R(b,c),(c,b)\in R

⇒(b,b)∈R,(c,c)∈R\Rightarrow (b,b)\in R,(c,c)\in R

7 elements must be added

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