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Q18A. Define the sets A and B as shown. Select all statements which are true. A W C {a, g, s, m} = A {a, f, g, h, m, s} = B {a, c, m, p, s, w} CA {m, s} = A {a, f} C B P S m a 6.0 g h f B

Q18A. Define the sets A and B as shown. Select all statements which are true. A W C {a, g, s, m} = A {a, f, g, h, m, s} = B {a, c, m, p, s, w} CA {m, s} = A {a, f} C B P S m a 6.0 g h f B

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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**Question 18A. Define the sets A and B as shown. Select all statements which are true.** The image depicts a Venn diagram consisting of two sets, A and B, which overlap. The elements in each region of the diagram are as follows: - **Set A (Left Circle):** - Exclusive to A: c, w, p - Shared with B: a, s, m - **Set B (Right Circle):** - Exclusive to B: g, f, h - Shared with A: a, s, m **Statements:** 1. \(\{a, g, s, m\} \subseteq A\) 2. \(\{a, f, g, h, m, s\} \subseteq B\) 3. \(\{a, c, m, p, s, w\} \subseteq A\) 4. \(\{m, s\} \subseteq A\) 5. \(\{a, f\} \subseteq B\)
Transcribed Image Text:**Question 18A. Define the sets A and B as shown. Select all statements which are true.** The image depicts a Venn diagram consisting of two sets, A and B, which overlap. The elements in each region of the diagram are as follows: - **Set A (Left Circle):** - Exclusive to A: c, w, p - Shared with B: a, s, m - **Set B (Right Circle):** - Exclusive to B: g, f, h - Shared with A: a, s, m **Statements:** 1. \(\{a, g, s, m\} \subseteq A\) 2. \(\{a, f, g, h, m, s\} \subseteq B\) 3. \(\{a, c, m, p, s, w\} \subseteq A\) 4. \(\{m, s\} \subseteq A\) 5. \(\{a, f\} \subseteq B\)
**Q17B. Define the sets A, B, C, and D as shown. Find \( A \cup (B \cap D) \).** **Diagram Explanation:** The Venn diagram consists of four sets, labeled A, B, C, and D. - **Set A** includes: c, w, s, m - **Set B** includes: p, a, g, f, h - **Set C** includes: s, m - **Set D** includes: a, g The Venn diagram visually shows the overlap and unique elements of these sets. To solve **\( A \cup (B \cap D) \):** 1. **B ∩ D** (intersection of B and D) includes elements common to both B and D: a, g 2. **A ∪ (B ∩ D)** (union of A and the intersection of B and D) includes all elements in A or in the intersection of B and D: \{a, c, g, m, s, w\} **Note:** - Express the set using roster notation with letters ordered alphabetically, such as \{d, n, x, z\}. - Braces and commas are required, with a space after each comma.
Transcribed Image Text:**Q17B. Define the sets A, B, C, and D as shown. Find \( A \cup (B \cap D) \).** **Diagram Explanation:** The Venn diagram consists of four sets, labeled A, B, C, and D. - **Set A** includes: c, w, s, m - **Set B** includes: p, a, g, f, h - **Set C** includes: s, m - **Set D** includes: a, g The Venn diagram visually shows the overlap and unique elements of these sets. To solve **\( A \cup (B \cap D) \):** 1. **B ∩ D** (intersection of B and D) includes elements common to both B and D: a, g 2. **A ∪ (B ∩ D)** (union of A and the intersection of B and D) includes all elements in A or in the intersection of B and D: \{a, c, g, m, s, w\} **Note:** - Express the set using roster notation with letters ordered alphabetically, such as \{d, n, x, z\}. - Braces and commas are required, with a space after each comma.
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