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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Sets and Relations

JEE Main · Mathematics · Sets and Relations

If A and B are any two events of a sample space, then set-theoretic...

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}

)

Options

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 $(A \cap B)^c \cup \left(A^c \cap B^c\right)$

Correct answer

C. $\left(A \cap B^c\right) \cup \left(A^c \cap B\right)$

Step-by-step 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)

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