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NDA 2026 · PYQ · Set Theory · medium

Let A and B be two sets. For some set C, both A ∩ C and B ∩ C are empty sets and A ∪ C = B ∪ C. Which of the following is/are correct? I. C = φ II. A = B III. A ∪ B = C. Select the correct answer using the code given below:

  1. A.I only
  2. B.II only✓ Correct
  3. C.I and II only
  4. D.I, II and III

Explanation

From A ∪ C = B ∪ C and A ∩ C = B ∩ C = φ, the elements of A (which are not in C) must equal elements of B (which are not in C). So A = B. Statement I (C = φ) need not be true — C can be any set disjoint from both A and B. Statement III is false for the same reason. Only II is correct.
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