If | A |= 50, | A ∩ B |= 44 and | B |= 58 then what is | P(A − B) |?

We are given the following information:

- \( |A| = 50 \), which is the size of set \( A \).
- \( |A \cap B| = 44 \), which is the size of the intersection of sets \( A \) and \( B \).
- \( |B| = 58 \), which is the size of set \( B \).

We need to find \( |P(A - B)| \), which is the size of the set \( A - B \) (the elements in \( A \) but not in \( B \)).

The formula for \( |A - B| \) is:
\[
|A - B| = |A| - |A \cap B|
\]

Substituting the given values:
\[
|A - B| = 50 - 44 = 6
\]

Thus, \( |A - B| = 6 \).

Therefore, the number of elements in \( A - B \) is \( 6 \).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you compute \( |A \cup B| \) given \( |A| \), \( |B| \), and \( |A \cap B| \)?
2. What is the formula for \( |A \cup B| \) when \( A \) and \( B \) are disjoint sets?
3. How can you find \( |B - A| \) using the information given?
4. If \( A \) and \( B \) are subsets of a universal set \( U \), how can you compute \( |A^c \cap B^c| \)?
5. What is the relationship between \( |A - B| \) and \( |B - A| \)?

**Tip**: Always remember that \( A - B \) refers to the elements in \( A \) that are not in \( B \).

If |A| = 50, |A ∩ B| = 44 and |B| = 58 then what is |P(A − B)|?

Learn how to find the number of elements in the set difference |A - B| using the given values of |A| = 50, |A ∩ B| = 44, and |B| = 58. This problem demonstrates key concepts in set theory and basic set operations, suitable for students in Grades 9-12.

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