Q78 / 160 · AP EAMCET 2023 (17 May Shift 1) · Mathematics
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$(A-B) \cup(A \cup B)$
- Correct answerC$\left(A \cap B^c\right) \cup\left(A^c \cap B\right)$
- D$(A \cap B)^c \cup\left(A^c \cap B^c\right)$
Solution
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 : $\left(A \cap B^C\right) \cup\left(A^C \cap B\right)$
Hence, the correct answer is option: 'C'.