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JEE Main20258 Apr 2025Evening ShiftMathematicsSets and RelationsActual

Let A= 0,1,2,3,4,5 . Let R be a relation on A defined by (x, y) R if and only if max x, y 3,4 . Then among the statements ( S ₁ ) : The number of elements in R is 18 , and ( S ₂ ) : The relation R is symmetric but neither reflexive nor transitive

Options

  1. Aboth are true
  2. Bboth are false
  3. Conly ( S ₂ ) is true
  4. Donly ( S ₁ ) is true

Correct answer

C. only ( S ₂ ) is true

Step-by-step solution

A= 0,1,2,3,4,5 R (0,3),(3,0),(0,4),(4,0),(1,3),(3,1),(1,4) , (4,1),(2,3),(3,2),(2,4),(4,2),(3,3),(3,4),(4,3) , (4,4) Total 16 elements Not reflexive as (0,0), ,(2,2) R Symmetric all a,b (a, b) &(b, a) R Not transitive (0,3),(3,1) R but (0,1) R Only S ₂ correct

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