Let ‘A’ stand for the set of students who like dancing. Let ‘B’ stand for the set of students who like music. Applying set theory we get n(A∪B)=n(A)+n(B)−n(A∩B) (60−5)=45+50−n(A∩B) n(A∩B)=95−55 n(A∩B)=40 Hence the set of students who like both are 40.