List the elements of the following sets; M%3DThe letters in the isordu mathematics= word" Note: There Ore not ll elements in the set. 11 b.) M-B when M is defined albove and B is defined aboe and B 0, (. :)AUB {se with B delined above and A=
List the elements of the following sets; M%3DThe letters in the isordu mathematics= word" Note: There Ore not ll elements in the set. 11 b.) M-B when M is defined albove and B is defined aboe and B 0, (. :)AUB {se with B delined above and A=
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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Transcribed Image Text:**Title: Understanding Set Operations and Examples**
In this section, we explore various set operations by listing elements of given sets and performing specified operations.
1. **Set Definition and Elements:**
- **a) Set M**: M represents the letters in the word "mathematics".
- Elements: {m, a, t, h, e, i, c, s}
- *Note: There are not 11 unique elements in this set, due to repetition of letters.*
2. **Set Operations:**
- **b) M - B**: The set difference between M and B where B = {a, e, i, o, u}.
- Result: {m, t, h, c, s}
- **c) A ∪ B**: The union of set A and set B, where A = {s, e, t}.
- Result: {s, e, t, a, i, o, u}
- **d) (A - B)**: The set difference between A and B with A representing the letters in the word "Sarina".
- Result: {S, r, n} (assuming A = {s, a, r, i, n})
3. **Power Set:**
- **e) A¹**: The power set of X where X = {a, b, c, d, ..., m}.
- A¹ includes all subsets of X.
4. **Element Existence in Sets:**
- **f) ∃ X ∈ Reals | X² + 6X + 8 = 0**: This represents checking the existence of real number solutions to the quadratic equation X² + 6X + 8 = 0.
- Solutions can be found using factorization or the quadratic formula.
This exercise demonstrates elementary set operations such as union, difference, power set, and the existence of solutions within a given context.
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