To solve the problem, we use the inclusion-exclusion principle for sets, which states:

Formula

For any two sets (A) and (B):
[|A \cup B| = |A| + |B| - |A \cap B|]

Given

• (|A| = 10) (number of elements in set (A))
• (|B| = 15) (number of elements in set (B))
• (|A \cup B| = 20) (number of elements in the union of (A) and (B))

Rearrange to find (|A \cap B|)

[|A \cap B| = |A| + |B| - |A \cup B|]

Calculate

[|A \cap B| = 10 + 15 - 20 = 5]

Answer: (\boxed{5})

作者声明:本文包含人工智能生成内容。