AP EAMCET · Maths · Sets and Relations
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
(Here \(\mathrm{E}^{\mathrm{c}}\) denotes the compliment of the event \(\mathrm{E}\) )
- A \(A \cap B^c\)
- B \((A-B) \cup(A \cup B)\)
- C \(\left(A \cap B^c\right) \cup\left(A^c \cap B\right)\)
- D \((A \cap B)^c \cup\left(A^c \cap B^c\right)\)
Answer & Solution
Correct Answer
(C) \(\left(A \cap B^c\right) \cup\left(A^c \cap B\right)\)
Step-by-step Solution
Detailed explanation
When only event \(A\) occurs, then it can be written as \(\left(A \cap B^C\right)\) And when only event B occurs, then it can be written as \(\left(A^C \cap B\right)\) Then, 'exactly one of the events \(A, B\) to occur' can be written as :…
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