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Check the boxes in the accompanying figures to indicate which regions should be shaded to represent each set. (Sel (a) AU (BN C)c U b) (A UBUC)

Check the boxes in the accompanying figures to indicate which regions should be shaded to represent each set. (Sel (a) AU (BN C)c U b) (A UBUC)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Venn Diagram Representation of Set Operations This image illustrates two Venn diagrams used to identify specific regions corresponding to given set operations. #### Diagram (a): \( A \cup (B \cap C)^C \) **Description:** - **Sets:** The diagram consists of three circles labeled \(A\), \(B\), and \(C\) within a rectangle that represents the universal set \(U\). - **Operation:** The expression \( A \cup (B \cap C)^C \) denotes the union of set \(A\) with the complement of the intersection between sets \(B\) and \(C\). **Highlighted Regions:** - The checked regions include: - Parts of \(A\) that do not overlap with \(B\) or \(C\). - Parts of circles \(B\) and \(C\) that are not part of their intersection. - The remaining area within the universal set \(U\) that does not intersect with any of the three sets. #### Diagram (b): \((A \cup B \cup C)^C\) **Description:** - **Sets:** This diagram also includes three circles labeled \(A\), \(B\), and \(C\) within a rectangle representing the universal set \(U\). - **Operation:** The expression \((A \cup B \cup C)^C\) represents the complement of the union of sets \(A\), \(B\), and \(C\). **Highlighted Regions:** - The checked region consists of the area outside the three circles \(A\), \(B\), and \(C\), indicating what is not part of any of the three sets, within the universal set \(U\). These diagrams are crucial for understanding basic set operations, including intersection, union, and complement, through visual aids.
Transcribed Image Text:### Venn Diagram Representation of Set Operations This image illustrates two Venn diagrams used to identify specific regions corresponding to given set operations. #### Diagram (a): \( A \cup (B \cap C)^C \) **Description:** - **Sets:** The diagram consists of three circles labeled \(A\), \(B\), and \(C\) within a rectangle that represents the universal set \(U\). - **Operation:** The expression \( A \cup (B \cap C)^C \) denotes the union of set \(A\) with the complement of the intersection between sets \(B\) and \(C\). **Highlighted Regions:** - The checked regions include: - Parts of \(A\) that do not overlap with \(B\) or \(C\). - Parts of circles \(B\) and \(C\) that are not part of their intersection. - The remaining area within the universal set \(U\) that does not intersect with any of the three sets. #### Diagram (b): \((A \cup B \cup C)^C\) **Description:** - **Sets:** This diagram also includes three circles labeled \(A\), \(B\), and \(C\) within a rectangle representing the universal set \(U\). - **Operation:** The expression \((A \cup B \cup C)^C\) represents the complement of the union of sets \(A\), \(B\), and \(C\). **Highlighted Regions:** - The checked region consists of the area outside the three circles \(A\), \(B\), and \(C\), indicating what is not part of any of the three sets, within the universal set \(U\). These diagrams are crucial for understanding basic set operations, including intersection, union, and complement, through visual aids.
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