F and H are sets of real numbers defined as follows. F={w|w<3} H={w | w≤9} Write FU H and FN H using interval notation. If the set is empty, write Ø. FUH = 0 FOH = 0 (0,0) [0,0] (0,0) [0,0) Ø ∞ X -8 Ś
F and H are sets of real numbers defined as follows. F={w|w<3} H={w | w≤9} Write FU H and FN H using interval notation. If the set is empty, write Ø. FUH = 0 FOH = 0 (0,0) [0,0] (0,0) [0,0) Ø ∞ X -8 Ś
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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![### F and H are sets of real numbers defined as follows.
\[ F = \{w \mid w < 3\} \]
\[ H = \{w \mid w \leq 9\} \]
Write \( F \cup H \) and \( F \cap H \) using **interval notation**.
If the set is **empty**, write \(\emptyset\).
#### Interval Notation
In interval notation, ranges of numbers are denoted using parentheses \(( \)) for open intervals and brackets \([ ]\) for closed intervals. For example, the set of all real numbers less than 3 is written as \((-\infty, 3)\), and the set of all real numbers less than or equal to 9 is written as \((-\infty, 9]\).
### Solution
#### For the Union (\( F \cup H \)):
The union of two sets \( F \) and \( H \) includes all elements from both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the union \( F \cup H \) will be:
\[ F \cup H = (-\infty, 9] \]
#### For the Intersection (\( F \cap H \)):
The intersection of two sets \( F \) and \( H \) includes only the elements that are common to both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the intersection \( F \cap H \) will be:
\[ F \cap H = (-\infty, 3) \]
#### Representation
1. \( F \cup H = (-\infty, 9] \)
2. \( F \cap H = (-\infty, 3) \)
### Diagram Explanation
In the provided diagram, there is an input area to select the correct interval notation for the union and intersection of the sets \( F \) and \( H \).
- Ensure to select:
- For \( F \cup H \), choose the interval notation representing \((-\infty, 9]\).
- For \( F \cap H \), choose the interval notation representing \((-\infty, 3)\).
This](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec8216c7-9603-414d-880e-1b2c9e8c3a03%2F2cd39673-6663-424c-9f9b-d727a2d20a8a%2F382mlwe_processed.png&w=3840&q=75)
Transcribed Image Text:### F and H are sets of real numbers defined as follows.
\[ F = \{w \mid w < 3\} \]
\[ H = \{w \mid w \leq 9\} \]
Write \( F \cup H \) and \( F \cap H \) using **interval notation**.
If the set is **empty**, write \(\emptyset\).
#### Interval Notation
In interval notation, ranges of numbers are denoted using parentheses \(( \)) for open intervals and brackets \([ ]\) for closed intervals. For example, the set of all real numbers less than 3 is written as \((-\infty, 3)\), and the set of all real numbers less than or equal to 9 is written as \((-\infty, 9]\).
### Solution
#### For the Union (\( F \cup H \)):
The union of two sets \( F \) and \( H \) includes all elements from both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the union \( F \cup H \) will be:
\[ F \cup H = (-\infty, 9] \]
#### For the Intersection (\( F \cap H \)):
The intersection of two sets \( F \) and \( H \) includes only the elements that are common to both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the intersection \( F \cap H \) will be:
\[ F \cap H = (-\infty, 3) \]
#### Representation
1. \( F \cup H = (-\infty, 9] \)
2. \( F \cap H = (-\infty, 3) \)
### Diagram Explanation
In the provided diagram, there is an input area to select the correct interval notation for the union and intersection of the sets \( F \) and \( H \).
- Ensure to select:
- For \( F \cup H \), choose the interval notation representing \((-\infty, 9]\).
- For \( F \cap H \), choose the interval notation representing \((-\infty, 3)\).
This
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