Math  /  Word Problems

QuestionFind the number of elements in Region III of a Venn diagram with sets A, B, and C given their sizes and intersections.

Studdy Solution
Calculate the number of elements in Region III.
n(U)[n(A)n(AB)n(AC)+n(ABC)][n(B)n(AB)n(BC)+n(ABC)][n(C)n(AC)n(BC)+n(ABC)]n(ABC)n(I)n(II)=9n(U) - [n(A) - n(A \cap B) - n(A \cap C) + n(A \cap B \cap C)] - [n(B) - n(A \cap B) - n(B \cap C) + n(A \cap B \cap C)] - [n(C) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)] - n(A \cap B \cap C) - n(I) - n(II) =9Region III contains9 elements.

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