Question
Consider the following statements in respect of the events A, B, C : I. (A B C) ( A B C ) is an impossible event. II. (A B C) ( A B C ) is a possible event. Which of the statements given above is/are correct ?
NDA
Mathematics
Probability
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II
Answer
A. I only
Step-by-step solution
Using De Morgan's laws, we have A B C = A B C . Substituting this in the expression for Statement I: (A B C) ( A B C ) = (A B C) (A B C) = Since the intersection of an event and its complement is the empty set , it represents an impossible event. Thus, Statement I is correct. Again, using De Morgan's laws, we have A B C = A B C . Substituting this in the expression for Statement II: (A B C) ( A B C ) = (A B C) (A B C) = This is also an impossible event. Thus, Statement II is incorrect. Therefore, only Statement I is correct.
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