Exact intersection count

#inclusion-exclusion#exact count#sets

Statement

Given $|A|=10$ , $|B|=15$ , $|A\cup B|=20$ , compute $|A\cap B|$ .

Hint

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

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Compute. $|A\cap B|=10+15-20=5$ .

Conclusion. $|A\cap B|=5$ .