Let R be a relation on the set N of natural numbers defined by \( R = \{ (x, y) : x, y \in N \text{ and } x = y^3 \} \). 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 :
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
For symmetry, if x = y^3, it does not imply y = x^3 (e.g., 8 = 2^3 but 2 != 8^3). For transitivity, if x = y^3 and y = z^3, then x = (z^3)^3 = z^9 != z^3. Both are false.
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