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Use a Venn Diagram or Some Other Method to Obtain n(A∪B∪C)n ( A \cup B \cup C )

Question 57

Multiple Choice

Use a Venn diagram or some other method to obtain a formula for
n(A∪B∪C) n ( A \cup B \cup C ) in terms of n(A) n ( A ) , n(B) n ( B ) , n(C) n ( C ) , n(A∩B) n ( A \cap B ) , n(A∩C) n ( A \cap C ) , n(B∩C) n ( B \cap C ) , and n(A∩B∩C) n ( A \cap B \cap C ) .


A) n(A∪B∪C) =n(A) +n(B) +n(C) −n(A∩B) −n(A∩C) −n(B∩C) +n(A∩B∩C) n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C ) + n ( A \cap B \cap C )

B) n(A∪B∪C) =n(A) +n(B) +n(C) −n(A∩B) −n(A∩C) −n(B∩C) −n(A∩B∩C) n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C ) - n ( A \cap B \cap C )

C) n(A∪B∪C) =n(A) +n(B) +n(C) −n(A∩B∩C) n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B \cap C )

D) n(A∪B∪C) =n(A) +n(B) +n(C) +n(A∩B) +n(A∩C) +n(B∩C) −n(A∩B∩C) n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) + n ( A \cap B ) + n ( A \cap C ) + n ( B \cap C ) - n ( A \cap B \cap C )

E) n(A∪B∪C) =n(A) +n(B) +n(C) −n(A∩B) −n(A∩C) −n(B∩C) n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C )

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