# Set theory II

**Discrete Mathematics**Level 2

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

Options:

\(|A\cap B|+|B\cap C|+|C\cap A|-3(|A\cap B\cap C|)\)

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

\(|A\cap B|+|B\cap C|+|C\cap A|-2|A\cap B\cap C|\)

\(|A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|\)

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

|\(A\cup B\cup C\) |