# Set theory II

Which of the following sequence of set operations counts the number of elements that are in exactly one of $$A$$, $$B$$ or $$C$$?"

Options:

1. $$|A\cap B|+|B\cap C|+|C\cap A|-3(|A\cap B\cap C|)$$

2. $$|A|+|B|+|C|-2(|A\cap B|+|B\cap C|+|C\cap A|)+3|A\cap B\cap C|$$

3. $$|A\cap B|+|B\cap C|+|C\cap A|-2|A\cap B\cap C|$$

4. $$|A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|$$

5. $$|(A\cap B\cap C)\cup(A\cap B^{C}\cap C^{C})\cup(A^{C}\cap B\cap C^{C})\cup(A^{C}\cap B^{C}\cap C)|$$

6. |$$A\cup B\cup C$$ |

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