Three-set counts

#inclusion-exclusion#three sets#union

Statement

Given $|A|=20$ , $|B|=25$ , $|C|=15$ , $|A\cap B|=10$ , $|A\cap C|=8$ , $|B\cap C|=5$ , $|A\cap B\cap C|=3$ , compute $|A\cup B\cup C|$ .

Hint

Apply the three-set formula.

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Formula. $|A\cup B\cup C|=20+25+15-10-8-5+3=40$ .

Conclusion. $|A\cup B\cup C|=40$ .