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**Find expression for event "exactly one of A,B,C occurs"**

## Homework Statement

Let [itex]A,B,C \in F[/itex] be three arbitrary events. F is a σ-algebra. Find an expression for the event "exactly one of A,B,C occurs".

## The Attempt at a Solution

Define [itex]i,j,k[/itex] s.t. [itex]i,j,k \in \{1,2,3\} \wedge i \not= j \not=k[/itex]. Also, define [itex]M_1 := A, M_2 := B, M_3 := C[/itex].

Then the event in question is [itex]M_i \backslash (M_j \cup M_k) \forall i[/itex].

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Is this correct? I've never seen this "notation" used in my lecture slides so I'm not sure (I'm trying to get out of writing a silly amount of unions and then simplifying).

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