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 \(C\)?"


  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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