SOLUTION: In using Venn diagram Out of 100 students 33 students are taking English subjects only while 42 students are taking mathematics only. How many students are taking both English

Consider these three subsets:

    a) 33 students taking English only;

    b) 42 students taking Math only;

    c) taking both English and Math.


These subsets have empty intersections (obviously).

Taken together, they cover the entire set of 100 students.


Hence, the subset of those taking both English and Math counts exactly 100 - 33 - 42 students.