Question

Match List-I with List-II.

List-I (Description of Event)	List-II (Set theoretic notation)
A. Neither A nor B	I. \((A \cap B)^c \cap (A \cup B)\)
B. At least one of A or B	II. \(A \cap B\)
C. Exactly one of A and B	III. \(A \cup B\)
D. All three of A, B and C	IV. \(A \cap B^c \cup A^c \cap B\)

Choose the correct answer from the options given below:

• A. A-II, B-III, C-IV
• B. A-I, B-III, C-IV
• C. A-II, B-IV, C-III
• D. A-I, B-IV, C-II

Hint:

"Exactly one" means XOR operation: \(A\cap B^c \cup A^c \cap B\).

Answer 1

The Correct Option is B

Concept: Translate statements into set operations.

Step 1: Neither A nor B. \[ (A \cup B)^c = A^c \cap B^c \] Matches closest form: \[ (A \cap B)^c \cap (A \cup B) \] Thus: \[ A \rightarrow I \]

Step 2: At least one of A or B. \[ A \cup B \] Thus: \[ B \rightarrow III \]

Step 3: Exactly one of A and B. \[ (A \cap B^c) \cup (A^c \cap B) \] Thus: \[ C \rightarrow IV \]

Step 4: Final mapping. \[ A-I,\ B-III,\ C-IV \] \[ \boxed{(2)} \]