Let A and B be two sets. For some set C, both \( A \cap C \) and \( B \cap C \) are empty sets and \( A \cup C = B \cup C \). Which of the following is/are true ? I. \( C = \varphi \) II. A = B III. \( A \cup B = C \) Select the answer using the code given below :
- A. I only
- B. II only ✓
- C. I and II only
- D. I, II and III
Correct Answer: B. II only
Explanation
Taking the intersection of A with both sides of A \cup C = B \cup C gives A = A \cap B. Similarly, B = A \cap B. Hence A = B. C doesn't strictly need to be empty, just disjoint from A and B.
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