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: $|A \cup B| = |A| + |B| - |A \cap B|$