Which of the numbers x, y, z, or w must equal 0 if AUB = U? The number must equal zero if AUB = U.

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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**Question:**

Which of the numbers x, y, z, or w must equal 0 if A ∪ B = U?

**Diagram Explanation:**

The diagram is a Venn diagram consisting of two overlapping circles labeled A and B, contained within a rectangle labeled U. Each section of the diagram is labeled with a variable:

- **x**: The part of circle A that does not overlap with circle B.
- **y**: The part where circles A and B overlap.
- **z**: The part of circle B that does not overlap with circle A.
- **w**: The area outside both circles A and B, but within the rectangle U.

**Answer:**

The number **w** must equal zero if A ∪ B = U.
Transcribed Image Text:**Question:** Which of the numbers x, y, z, or w must equal 0 if A ∪ B = U? **Diagram Explanation:** The diagram is a Venn diagram consisting of two overlapping circles labeled A and B, contained within a rectangle labeled U. Each section of the diagram is labeled with a variable: - **x**: The part of circle A that does not overlap with circle B. - **y**: The part where circles A and B overlap. - **z**: The part of circle B that does not overlap with circle A. - **w**: The area outside both circles A and B, but within the rectangle U. **Answer:** The number **w** must equal zero if A ∪ B = U.
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