To solve the problem of naming the sets for the shaded regions in the given Venn diagrams, we need to use set notation. Here's a step-by-step explanation for each diagram:
1)
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Shaded region: The entire circle \( A \).
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Set notation: \( A \)
2)
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Shaded region: The intersection of \( A \) and \( B \).
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Set notation: \( A \cap B \)
3)
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Shaded region: The union of \( A \) and \( B \).
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Set notation: \( A \cup B \)
4)
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Shaded region: The part of \( A \) that is not in \( B \) (i.e., \( A \setminus B \)).
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Set notation: \( A \setminus B \) or \( A - B \)
5)
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Shaded region: The part of \( B \) that is not in \( A \) (i.e., \( B \setminus A \)).
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Set notation: \( B \setminus A \) or \( B - A \)
6)
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Shaded region: The union of \( A \) and \( B \), excluding their intersection (i.e., \( (A \cup B) \setminus (A \cap B) \)).
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Set notation: \( (A \cup B) \setminus (A \cap B) \) or \( A \Delta B \) (symmetric difference)
7)
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Shaded region: The complement of \( B \) (i.e., everything outside \( B \)).
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Set notation: \( B^c \) or \( U \setminus B \) (where \( U \) is the universal set)
8)
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Shaded region: The complement of \( A \) (i.e., everything outside \( A \)).
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Set notation: \( A^c \) or \( U \setminus A \) (where \( U \) is the universal set)
9)
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Shaded region: The complement of the union of \( A \) and \( B \) (i.e., everything outside both \( A \) and \( B \)).
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Set notation: \( (A \cup B)^c \) or \( U \setminus (A \cup B) \)
10)
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Shaded region: The intersection of \( A \) and \( C \), excluding \( B \) (i.e., \( (A \cap C) \setminus B \)).
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Set notation: \( (A \cap C) \setminus B \)
11)
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Shaded region: The union of \( A \), \( B \), and \( C \).
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Set notation: \( A \cup B \cup C \)
12)
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Shaded region: The intersection of \( A \), \( B \), and \( C \).
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Set notation: \( A \cap B \cap C \)
Final Answers:
1. \( A \)
2. \( A \cap B \)
3. \( A \cup B \)
4. \( A \setminus B \)
5. \( B \setminus A \)
6. \( (A \cup B) \setminus (A \cap B) \) or \( A \Delta B \)
7. \( B^c \)
8. \( A^c \)
9. \( (A \cup B)^c \)
10. \( (A \cap C) \setminus B \)
11. \( A \cup B \cup C \)
12. \( A \cap B \cap C \)
\[
\boxed{
\begin{array}{ccc}
1. & A & \\
2. & A \cap B & \\
3. & A \cup B & \\
4. & A \setminus B & \\
5. & B \setminus A & \\
6. & (A \cup B) \setminus (A \cap B) & \\
7. & B^c & \\
8. & A^c & \\
9. & (A \cup B)^c & \\
10. & (A \cap C) \setminus B & \\
11. & A \cup B \cup C & \\
12. & A \cap B \cap C &
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of set worksheet.
