Cardinality of Set Union/Examples/Student Subjects
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Example of Use of Cardinality of Set Union
In a particular group of $75$ students, all studied at least one of the subjects mathematics, physics and chemistry.
All candidates attempted at least one of the questions.
- $40$ students studied mathematics.
- $60$ students studied physics.
- $25$ students studied chemistry.
Also:
- exactly $5$ students studied all $3$ subjects.
It follows that:
Mathematics and Physics
- at least $25$ students studied both mathematics and physics.
Physics and Chemstry
- at least $10$ students studied both physics and chemistry.
Mathematics and Chemistry
- no more than $20$ students studied both mathematics and chemistry.
Sources
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems: Exercise $10$