Pregunta
Sets \( A \) and \( B \) are defined as follows. \( \begin{array}{l}A=\{d, e, j\} \\ B=\{a, e, h\}\end{array} \) Answer each part below. Write your answer in roster form or as \( \varnothing \). (a) Find the intersection of \( A \) and \( B \). \( A \cap B=\square \) (b) Find the union of \( A \) and \( B \). \( A \cup B=\square \)
Ask by Cervantes Maxwell. in the United States
Jan 26,2025
Solución de tutoría real
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\( A \cap B = \{e\} \)
\( A \cup B = \{a, d, e, h, j\} \)
Solución
Let's analyze the sets \( A \) and \( B \):
\[
A = \{d, e, j\} \\
B = \{a, e, h\}
\]
### (a) Intersection of \( A \) and \( B \) (\( A \cap B \))
The **intersection** of two sets consists of elements that are **common to both sets**.
- **Common Element:** \( e \)
\[
A \cap B = \{e\}
\]
### (b) Union of \( A \) and \( B \) (\( A \cup B \))
The **union** of two sets includes **all distinct elements** from both sets.
\[
A \cup B = \{a, d, e, h, j\}
\]
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**Final Answers:**
(a) \( A \cap B = \{e\} \)
(b) \( A \cup B = \{a, d, e, h, j\} \)
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The Deep Dive
To find the intersection and union of the sets \( A \) and \( B \): (a) The intersection \( A \cap B \) includes the elements that are common to both sets. Here, the only common element is \( e \). So, \[ A \cap B = \{ e \} \] (b) The union \( A \cup B \) includes all elements from both sets, without duplication. Therefore, we combine the elements from both sets: \[ A \cup B = \{ d, e, j, a, h \} \]
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