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JEE Main20244 Apr 2024Evening ShiftMathematicsSets and RelationsActual

Let a relation R on N N be defined as: (x₁, y₁ ) R (x₂, y₂ ) if and only if x₁ x₂ or y₁ y₂ . Consider the two statements: (I) R is reflexive but not symmetric. (II) R is transitive Then which one of the following is true?

Options

  1. ABoth (I) and (II) are correct.
  2. BOnly (II) is correct.
  3. CNeither (I) nor (II) is correct.
  4. DOnly (I) is correct.

Correct answer

D. Only (I) is correct.

Step-by-step solution

All ( ( x ₁ y ₁ ), ( x ₁, y ₁ ) ) are in R where x ₁, y ₁ N R is reflexive ((1,1),(2,3)) R but ((2,3),(1,1)) R R is not symmetric ((2,4),(3,3)) R and ((3,3),(1,3)) R but ((2,4) , (1,3)) R R is not transitive

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