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JEE Main202528 Jan 2025Morning ShiftMathematicsSets and RelationsActual

The relation R= (x, y): x, y Z and x+y is even is:

Options

  1. Areflexive and symmetric but not transitive
  2. Ban equivalence relation
  3. Csymmetric and transitive but not reflexive
  4. Dreflexive and transitive but not symmetric

Correct answer

B. an equivalence relation

Step-by-step solution

For reflexive (x, x) R , x Z x+x=2 x even For symmetric of (x, y) R then (y, x) R when x, y Z x+y even y+x even for transitive if (x, y) R x+y even (y, z) R y+z even x+2 y+z even x+z is even (x, z) R R is an equivalence relation.

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