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Set Theorymedium
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Let AAA, BBB, and CCC be three sets such that:

  • n(A)=10,n(B)=12,n(C)=14n(A) = 10, n(B) = 12, n(C) = 14n(A)=10,n(B)=12,n(C)=14
  • n(A∩B)=4,n(B∩C)=5,n(A∩C)=3n(A \cap B) = 4, n(B \cap C) = 5, n(A \cap C) = 3n(A∩B)=4,n(B∩C)=5,n(A∩C)=3
  • n(A∩B∩C)=2n(A \cap B \cap C) = 2n(A∩B∩C)=2 Determine the cardinality of their symmetric difference n(AΔBΔC)n(A \Delta B \Delta C)n(AΔBΔC).