Question
Sets \( E \) and \( F \) are defined as follows. \[ \begin{array}{l}E=\{-2,0,4,8\} \\ F=\{-1,3,4,5,8\}\end{array} \] Answer each part below. Write your answer in roster form or as \( \varnothing \). (a) Find the union of \( E \) and \( F \). \( E \cup F=\square \) (b) Find the intersection of \( E \) and \( F \). \( E \cap F=\square \)
Ask by Mcguire Osborne. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
(a) \( E \cup F = \{-2, -1, 0, 3, 4, 5, 8\} \)
(b) \( E \cap F = \{4, 8\} \)
Solution
Let's analyze the sets \( E \) and \( F \):
\[
E = \{-2, 0, 4, 8\}
\]
\[
F = \{-1, 3, 4, 5, 8\}
\]
### (a) Union of \( E \) and \( F \)
The union \( E \cup F \) consists of all elements that are in either \( E \) or \( F \) (or both), without repeating any elements.
\[
E \cup F = \{-2, -1, 0, 3, 4, 5, 8\}
\]
### (b) Intersection of \( E \) and \( F \)
The intersection \( E \cap F \) consists of all elements that are common to both \( E \) and \( F \).
\[
E \cap F = \{4, 8\}
\]
**Final Answers:**
(a) \( E \cup F = \{-2,\ -1,\ 0,\ 3,\ 4,\ 5,\ 8\} \)
(b) \( E \cap F = \{4,\ 8\} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Let's dive in! For the union of sets \( E \) and \( F \), we gather all unique elements from both sets. Thus, \( E \cup F = \{-2, 0, 3, 4, 5, 8\} \). Next, for the intersection, we identify the elements that appear in both sets. Hence, \( E \cap F = \{4, 8\} \). So, the answers are: (a) \( E \cup F = \{-2, 0, 3, 4, 5, 8\} \) (b) \( E \cap F = \{4, 8\} \)
