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COMEDK202510 May 2025Evening ShiftMathematicsSets and RelationsActual

For real numbers x and y, x R y x-y+ 2 is an irrational number. Then the relation R is:

Options

  1. ATransitive
  2. BEquivalence
  3. CSymmetric
  4. DReflexive

Correct answer

D. Reflexive

Step-by-step solution

Reflexive: For xRx , substitute y = x : x - x + 2 = 2 , which is irrational. So R is reflexive. Symmetric: Let x = 2 , y = 0 . xRy : 2 - 0 + 2 = 2 2 (irrational) True yRx : 0 - 2 + 2 = 0 (rational) False So R is not symmetric. Transitive: Let x = 2 , y = 0 , z = 2 2 . xRy : 2 - 0 + 2 = 2 2 (irrational) True yRz : 0 - 2 2 + 2 = - 2 (irrational) True xRz : 2 - 2 2 + 2 = 0 (rational) False So R is not transitive. Since R is neither symmetric nor transitive, it is not an equivalence relation. R is only Reflexive.

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