Consider the following statements in respect of the events A, B, C : I. \( (A \cup B \cup C) \cap (\overline{A} \cap \overline{B} \cap \overline{C}) \) is an impossible event. II. \( (A \cap B \cap C) \cap (\overline{A} \cup \overline{B} \cup \overline{C}) \) is a possible event. Which of the statements given above is/are correct ?
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
Statement I is the intersection of a union and its exact complement, which is empty (impossible). Statement II is the intersection of an intersection and its exact complement (by De Morgan's Law), which is also empty (impossible). Therefore, only I is correct.
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