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In Problems 17-24, use the given information to determine the number of elements in each of the four disjoint subsets in the fol- lowing Venn diagram. U A B ANBANBA'NB A' B' 17. n(A) = 100, n(B) = 90, n(ANB) = 50, n(U) = 200 18. n(A) = 40, n(B) = 60, n(AB) = 20, n(U) = 100 100

In Problems 17-24, use the given information to determine the number of elements in each of the four disjoint subsets in the fol- lowing Venn diagram. U A B ANBANBA'NB A' B' 17. n(A) = 100, n(B) = 90, n(ANB) = 50, n(U) = 200 18. n(A) = 40, n(B) = 60, n(AB) = 20, n(U) = 100 100

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please help me solve problem 18
### Venn Diagrams and Set Operations In Problems 17-24, use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram. #### Venn Diagram Explanation: The Venn diagram consists of two overlapping circles labeled \( A \) and \( B \) within the universal set \( U \). The regions are defined as follows: - \( A \cap B' \) (Elements in \( A \) but not in \( B \)): Shaded in blue. - \( A \cap B \) (Elements in both \( A \) and \( B \)): Shaded in purple. - \( A' \cap B \) (Elements in \( B \) but not in \( A \)): Shaded in yellow. - \( A' \cap B' \) (Elements not in \( A \) or \( B \)): Shaded in green. #### Problems and Solutions: **17.** - \( n(A) = 100 \) - \( n(B) = 90 \) - \( n(A \cap B) = 50 \) - \( n(U) = 200 \) **18.** - \( n(A) = 40 \) - \( n(B) = 60 \) - \( n(A \cap B) = 20 \) - \( n(U) = 100 \) **19.** - \( n(A) = 35 \) - \( n(B) = 85 \) - \( n(A \cup B) = 90 \) - \( n(U) = 100 \) **20.** - \( n(A) = 65 \) - \( n(B) = 150 \) - \( n(A \cup B) = 175 \) - \( n(U) = 200 \) **21.** - \( n(A') = 110 \) - \( n(B') = 220 \) - \( n(A' \cap B') = 60 \) - \( n(U) = 300 \) **22.** - \( n(A') = 70 \) - \( n(B') = 170 \) - \( n(A' \cap B') = 40 \) - \( n(U) = 300 \) **23.** - \( n(A') = 20 \) - \( n(B') =
Transcribed Image Text:### Venn Diagrams and Set Operations In Problems 17-24, use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram. #### Venn Diagram Explanation: The Venn diagram consists of two overlapping circles labeled \( A \) and \( B \) within the universal set \( U \). The regions are defined as follows: - \( A \cap B' \) (Elements in \( A \) but not in \( B \)): Shaded in blue. - \( A \cap B \) (Elements in both \( A \) and \( B \)): Shaded in purple. - \( A' \cap B \) (Elements in \( B \) but not in \( A \)): Shaded in yellow. - \( A' \cap B' \) (Elements not in \( A \) or \( B \)): Shaded in green. #### Problems and Solutions: **17.** - \( n(A) = 100 \) - \( n(B) = 90 \) - \( n(A \cap B) = 50 \) - \( n(U) = 200 \) **18.** - \( n(A) = 40 \) - \( n(B) = 60 \) - \( n(A \cap B) = 20 \) - \( n(U) = 100 \) **19.** - \( n(A) = 35 \) - \( n(B) = 85 \) - \( n(A \cup B) = 90 \) - \( n(U) = 100 \) **20.** - \( n(A) = 65 \) - \( n(B) = 150 \) - \( n(A \cup B) = 175 \) - \( n(U) = 200 \) **21.** - \( n(A') = 110 \) - \( n(B') = 220 \) - \( n(A' \cap B') = 60 \) - \( n(U) = 300 \) **22.** - \( n(A') = 70 \) - \( n(B') = 170 \) - \( n(A' \cap B') = 40 \) - \( n(U) = 300 \) **23.** - \( n(A') = 20 \) - \( n(B') =
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