Q15C. Define the sets A, B, C, and D as follows: A={yEZ:2
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 26E: Determine whether the set S={2x+x2,8+x3,x2+x3,4+x2} spans P3.
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Transcribed Image Text:**Q15C. Define the sets A, B, C, and D as follows:**
- \( A = \{ y \in \mathbb{Z} : 2 < y \leq 9 \text{ and } y \text{ is odd} \} \).
- \( B = \{ 1, 4, 6 \} \).
- \( C = \{ y \in \mathbb{Z} : y \leq 10, y \text{ is even, and } y \text{ is positive} \} \).
- \( D = \{ y \in \mathbb{Z} : y \leq 7 \text{ and } y \text{ is positive} \} \).
- \( E = \{ -3, -1, 0, 5 \} \).
**Find \( C \cup D \).**
*Express the set using roster notation and with values ordered smallest to largest, such as \(\{-10, -3, 1, 6\}\) (braces and commas are required; a space after each comma is also required).*

Transcribed Image Text:**Question 16C**: Define the sets A and B as shown. **Find A - B.**
In the diagram, two sets A and B are represented as overlapping circles in a Venn diagram.
- **Set A** contains the elements: c, w, p, a, s, m.
- **Set B** contains the elements: a, s, m, g, f, h.
- The intersection of sets A and B (shared area) contains the elements: a, s, m.
To find **A - B** (the relative complement of B in A), we identify the elements that are in A but not in the intersection of A and B.
**Elements in A - B**: c, w, p.
*Express the set using roster notation, and with letters ordered alphabetically.*
So, **A - B** = {c, p, w}.
(Braces and commas are required; a space after each comma is also required.)
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