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The problem is about calculating the cardinality of a set difference involving complement sets.

**Given:**
- \( |A \cap B| = 30 \)
- \( |A \cup B| = 86 \)
- \( |A| = 42 \)
- \( |B| = 34 \)

**Goal:** Find \( |A' \setminus B| \), where \( A' \) represents the complement of \( A \).

### Solution:

1. **Calculate the universal set cardinality \( |U| \):**
   Since \( A' \) and \( B' \) relate to complements, we first need the cardinality of the universal set \( |U| \).
   
   From the union formula:
   \[
   |A \cup B| = |A| + |B| - |A \cap B|
   \]
   Substitute the values:
   \[
   86 = 42 + 34 - 30
   \]
   So, the values are consistent, and \( |U| = 86 \).

2. **Calculate \( |A'| \):**
   The complement \( A' \) represents elements not in \( A \), so:
   \[
   |A'| = |U| - |A| = 86 - 42 = 44
   \]

3. **Calculate \( |A' \cap B| \):**
   Use the formula:
   \[
   |A \cup B| = |A| + |B| - |A \cap B|
   \]


Про множини A і B відомо, що |A ∩ B| = 30, |A ∪ B| = 86, |A| = 42, |B| = 34. Знайдіть потужність булеану множини A' \ B.

Learn how to find the cardinality of the Boolean set difference A' \ B. This problem involves set theory concepts, including union, intersection, complement, and set difference. Suitable for high school students in Grades 10-12.

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