Set theory II

Probability Level 2

Which of the following sequence of set operations counts the number of elements that are in exactly one of AA, BB or CC?"


  1. AB+BC+CA3(ABC)|A\cap B|+|B\cap C|+|C\cap A|-3(|A\cap B\cap C|)

  2. A+B+C2(AB+BC+CA)+3ABC|A|+|B|+|C|-2(|A\cap B|+|B\cap C|+|C\cap A|)+3|A\cap B\cap C|

  3. AB+BC+CA2ABC|A\cap B|+|B\cap C|+|C\cap A|-2|A\cap B\cap C|

  4. A+B+CABBCCA+ABC|A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|

  5. (ABC)(ABCCC)(ACBCC)(ACBCC)|(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. |ABCA\cup B\cup C |


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