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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 true? I. C = φ II. A = B III. A ∪ B = C Select the 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

Given A ∩ C = φ and B ∩ C = φ, with A ∪ C = B ∪ C. Taking intersection with the complement of C on both sides, A = B. C need not be empty (C could be any set disjoint from both A and B). So only statement II is necessarily true.
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