Question

If A and B are any two events of a sample space, then set-theoretic description for the event "Exactly one of the events A, B to occur" is:

• A. \( A \cap B^c \)
• B. \( (A - B) \cup (A \cup B) \)
• C. \( (A \cap B^c) \cup (A^c \cap B) \)
• D. \( (A \cap B^c)^c \cup (A^c \cap B^c) \)

Hint:

To describe "exactly one" of two events using set theory, use the union of the event where one occurs and the other does not.

Answer 1

The Correct Option is C

The event "Exactly one of A or B occurs" is described by the union of two disjoint events: either A occurs and B does not, or B occurs and A does not. This is given by \( (A \cap B^c) \cup (A^c \cap B) \).