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JEE Main20246 Apr 2024Evening ShiftMathematicsSets and RelationsActual

Let A= 1,2,3,4,5 . Let R be a relation on A defined by x R y if and only if 4 x 5 y . Let m be the number of elements in R and n be the minimum number of elements from A A that are required to be added to R to make it a symmetric relation. Then m + n is equal to :

Options

  1. A25
  2. B24
  3. C26
  4. D23

Correct answer

A. 25

Step-by-step solution

Given : 4 x 5 y then aligned R = & (1,1),(1,2),(1,3),(1,4),(1,5),(2,2),(2,3),(2,4) & (2,5),(3,3),(3,4),(3,5),(4,4),(4,5),(5,4),(5,5) aligned i.e. 16 elements. i.e. m =16 Now to make R a symmetric relation add (2,1)(3,2)(4,3)(3,1)(4,2)(5,3)(4,1)(5,2)(5,1) i.e. n=9 So m+n=25

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