https://file.aiquickdraw.com/mathbot/file/17292817296552tqo6bx7.jpg

The Venn diagram in the image displays three sets \( A \), \( B \), and \( C \), with various regions indicating the cardinality of the elements in their intersections.

The problem asks for the value of \( n(A \cap B^c \cap C^c) \), which represents the number of elements in set \( A \) but not in sets \( B \) or \( C \). This is the part of \( A \) that does not overlap with \( B \) or \( C \).

Looking at the Venn diagram:

- The only region that belongs solely to set \( A \) (and does not intersect with \( B \) or \( C \)) is the part labeled **15**.

Thus, the value of \( n(A \cap B^c \cap C^c) \) is **15**.

Would you like a detailed explanation on set notation, or have any further questions?

Here are 5 related questions to expand your understanding:
1. What is the meaning of \( n(A \cap B) \) in set theory?
2. How do you find the cardinality of the union of two sets, \( A \cup B \)?
3. What is the significance of \( A^c \) in set theory?
4. How do Venn diagrams help visualize relationships between sets?
5. How would you calculate \( n(A \cup B \cup C) \) using a Venn diagram?

**Tip**: To solve set problems with Venn diagrams, it's crucial to carefully examine the regions corresponding to each combination of sets and intersections.

Find the cardinality of n(A ∩ B^c ∩ C^c) from the given Venn diagram.

Learn how to determine the value of n(A ∩ B^c ∩ C^c) using a Venn diagram. This problem involves key set theory concepts such as intersections, complements, and cardinality. Suitable for students in Grades 7-10.

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