I am having trouble finding expressions for the following. My attempts are separated from the question with a semicolon.
Let $A$, $B$, and $C$ be events. Find expressions for:
- only $A$ occurs; $A \cap \neg B \cap \neg C$
- only $A$ doesn't occur; $\neg A \cap B \cap C $
- $A$ and $B$ don't occur, but $C$ does; $\neg A \cap \neg B \cap C$
- $A$ and $B$ occur, but $C$ doesn't occur; $A \cap B \cap \neg C$
- at least one of $A$ and $B$, but not $C$ occurs; $(A \cup B) \cap \neg C $
- at least one of the events occur; $A \cup B \cup C$
- at least two of the events occur; $(A \cup B) \cup (B \cup C) \cup (C \cup A)$
- all three events occur; $A \cap B \cap C$
- none of the events occur; $\neg A \cap \neg B \cap \neg C$
- at most one of the events occurs; $(A - (A \cap B \cap C)) \cup (B - (A \cap B \cap C)) \cup (C - (A\cap B\cap C))$ .
Could someone please let me know if my reasoning is correct?