Question
Sets \( H \) and \( L \) are defined as follows. \( \begin{array}{l}H=\{f, g, j\} \\ L=\{g, h, j\}\end{array} \) Answer each part below. Write your answer in roster form or as \( \varnothing \). \( \begin{array}{l}\text { (a) Find the intersection of } H \text { and } L . \\ H \cap L=\square \\ \text { (b) Find the union of } H \text { and } L .\end{array} \) \( H \cup L=\square \)
Ask by Kelley Mitchell. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( H \cap L = \{g, j\} \)
\( H \cup L = \{f, g, h, j\} \)
Solution
Let's analyze the sets \( H \) and \( L \):
\[
H = \{f, g, j\} \\
L = \{g, h, j\}
\]
### (a) Intersection of \( H \) and \( L \)
The intersection \( H \cap L \) contains all elements that are present in both \( H \) and \( L \).
- Common elements in both sets: \( g \) and \( j \).
\[
H \cap L = \{g, j\}
\]
### (b) Union of \( H \) and \( L \)
The union \( H \cup L \) contains all elements that are present in either \( H \) or \( L \).
- Elements in \( H \): \( f, g, j \)
- Elements in \( L \): \( g, h, j \)
- Combined without repetition: \( f, g, h, j \)
\[
H \cup L = \{f, g, h, j\}
\]
**Final Answers:**
- **(a)** \( H \cap L = \{g, j\} \)
- **(b)** \( H \cup L = \{f, g, h, j\} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
For part (a), the intersection of the sets \( H \) and \( L \) includes only the elements that are common to both sets. Here, the common elements are \( g \) and \( j \). So, we have: \( H \cap L = \{g, j\} \) For part (b), the union of the sets \( H \) and \( L \) consists of all unique elements present in either set. The combined elements from both sets are \( f, g, h, j \). Thus, we find: \( H \cup L = \{f, g, h, j\} \)
