Exactly one of two properties

#IE#exactly one#properties

Statement

Among $100$ students, $60$ study Spanish, $50$ study German, $30$ study both. How many study exactly one language?

Hint

$|A\triangle B|=|A|+|B|-2|A\cap B|$ .

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Compute. $60+50-2\cdot30=50$ .

Conclusion. $50$ study exactly one language.

Check. Spanish only: $30$ ; German only: $20$ ; total $50$ . ✓