Exact intersection count

#IE#intersection#count

Statement

Given $|A|=20$ , $|B|=25$ , $|A\cup B|=35$ , compute $|A\cap B|$ .

Hint

Rearrange the two-set formula.

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Rearrange. $|A\cap B|=|A|+|B|-|A\cup B|=20+25-35=10$ .

Conclusion. $|A\cap B|=10$ .