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NDA 2026 · PYQ · Relations and Functions · medium

Let R be a relation on the set N of natural numbers defined by R = {(x, y) : x, y ∈ N and x = y³}. Which of the following statements is/are correct? I. R is symmetric relation II. R is transitive relation. Select the answer using the code given below:

  1. A.I only
  2. B.II only
  3. C.Both I and II
  4. D.Neither I nor II✓ Correct

Explanation

If (x, y) ∈ R, then x = y³. For symmetry, we'd need y = x³, but x = y³ doesn't imply y = x³ in general. So not symmetric. For transitivity, if x = y³ and y = z³, then x = z⁹ ≠ z³ in general. So not transitive. Neither holds.
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