Cardinality of Set Union/Examples/Student Subjects

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:

at least $25$ students studied both mathematics and physics.

at least $10$ students studied both physics and chemistry.

no more than $20$ students studied both mathematics and chemistry.

1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems: Exercise $10$