A 12 7 22 11 27 17 28 23 8 В E 1 18 13 16 6 31 29 /24 26 /21 19/ 20 30 32 15 10 25 14 4 C 3.
A 12 7 22 11 27 17 28 23 8 В E 1 18 13 16 6 31 29 /24 26 /21 19/ 20 30 32 15 10 25 14 4 C 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Using the Venn diagram in the figure, specify which region is described by the following statements.
(a)
(b)
| A ∪ B ∪ C ∪ D ∪ E |
(b)
| A ∩ | B ∪ C ∪ D ∪ E |
Transcribed Image Text:The image displays a five-set Venn diagram, featuring sets labeled A, B, C, D, and E. Each set is represented by an oval shape, with the intersections numbered to show the relationships between the sets. The numbers indicate the different regions, demonstrating how elements can belong to multiple sets simultaneously.
- Set A (Red Oval): Covers unique elements 2, 7, and 12. Intersects with other sets showing shared elements.
- Set B (Purple Oval): Contains unique elements 3 and 8. Intersects with other sets for shared elements.
- Set C (Yellow Oval): Contains unique element 4 and intersects with various sets for shared elements.
- Set D (Green Oval): Contains unique elements 5 and 10. It intersects with other sets for shared membership.
- Set E (Pink Oval): Contains unique element 1 and intersects with various other sets.
In the intersection of all five sets (A, B, C, D, and E), the number 31 is present, showing a common element shared by all sets. Other intersections show various overlaps, such as:
- A ∩ B contains 12.
- A ∩ C contains 14.
- A ∩ D contains 15.
- A ∩ E contains 11.
- B ∩ C contains 13.
- B ∩ D contains 9.
- B ∩ E contains 6.
- C ∩ D contains 25.
- C ∩ E contains 24.
- D ∩ E contains 26.
And many other combinations, indicating dynamic interactions between the sets. The number 32 is outside all the sets, indicating an element belonging to none.
This diagram serves as a visual tool to understand complex relationships and intersections among multiple sets in set theory.
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