Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![### Set Theory and Elements
**List the elements of the following sets:**
a) **\( M = \text{The letters in the word "mathematics"} \)**
- **Note:** There are not 11 elements in the set.
- **Solution:** \( M = \{ m, a, t, h, e, i, c, s \} \)
b) **\( M - B \) when \( M \) is defined above and \( B = \{ a, e, i, o, u \} \)**
- **Solution:** \( M - B = \{ m, t, h, c, s \} \)
c) **\( A \cup B \) with \( B \) defined above and \( A = \{ s, e, t \} \)**
- **Solution:** \( A \cup B = \{ s, e, t, a, i, o, u \} \)
d) **\( (A - B) \) for \( A \) and \( B \) defined above with**
- **The letters in the word "Sarina"**
- **Solution:** \( A - B = \{ s, t \} \) and "Sarina" leads to \\{ s, a, r, i, n \}.
e) **\( A^t \) when \( x = \{ a, b, c, d, \ldots, m \} \)**
- **Interpretation:** Elements of \( x \) are not defined in detail.
f) **\( x \in \text{Reals} \), solve \( x^2 + 6x + 8 = 0 \)**
- **Solution:** Solve the quadratic equation \( x^2 + 6x + 8 = 0 \) using the quadratic formula or factoring:
\[
(x + 2)(x + 4) = 0
\]
Hence, \( x = -2 \) or \( x = -4 \).](https://content.bartleby.com/qna-images/question/7dbb4ae4-0d65-4baa-9481-63f79be91eca/c1f8da9f-ff79-4533-923c-e0d330b6a236/yecupgp.jpeg)
Transcribed Image Text:### Set Theory and Elements
**List the elements of the following sets:**
a) **\( M = \text{The letters in the word "mathematics"} \)**
- **Note:** There are not 11 elements in the set.
- **Solution:** \( M = \{ m, a, t, h, e, i, c, s \} \)
b) **\( M - B \) when \( M \) is defined above and \( B = \{ a, e, i, o, u \} \)**
- **Solution:** \( M - B = \{ m, t, h, c, s \} \)
c) **\( A \cup B \) with \( B \) defined above and \( A = \{ s, e, t \} \)**
- **Solution:** \( A \cup B = \{ s, e, t, a, i, o, u \} \)
d) **\( (A - B) \) for \( A \) and \( B \) defined above with**
- **The letters in the word "Sarina"**
- **Solution:** \( A - B = \{ s, t \} \) and "Sarina" leads to \\{ s, a, r, i, n \}.
e) **\( A^t \) when \( x = \{ a, b, c, d, \ldots, m \} \)**
- **Interpretation:** Elements of \( x \) are not defined in detail.
f) **\( x \in \text{Reals} \), solve \( x^2 + 6x + 8 = 0 \)**
- **Solution:** Solve the quadratic equation \( x^2 + 6x + 8 = 0 \) using the quadratic formula or factoring:
\[
(x + 2)(x + 4) = 0
\]
Hence, \( x = -2 \) or \( x = -4 \).
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