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= II. A=B III. A B=C Select the answer using the code given below :

NDA 2026 Mathematics question

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

(A)I only
(B)II onlyCorrect
(C)I and II only
(D)I, II and III

Answer: (B)

Solution

Since , ; similarly . As , we get , so II is true. I need not hold: e.g. , $C =

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Question ID VK-030276