In a class of 40 students, 12 enrolled for both Italian and French. 22 enrolled for French. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only Italian and not French?
In a class of 40 students, 12 enrolled for both Italian and French. 22 enrolled for French. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only Italian and not French?
The correct option is C 18
(c) Let A be the set of students who have enrolled for Italian and B be the set of students who have enrolled for French. Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40
We know A U B = A + B - (A n B) i.e, 40 = A + 22 – 12 or
A = 30 which is the set of students who have enrolled for Italian and includes those who have enrolled for both the subjects.
However, we need to find out the number of students who have enrolled for only Italian = Students enrolled for Italian - Students enrolled for both French and Italian = 30 - 12 = 18.
18
(c) Let A be the set of students who have enrolled for Italian and B be the set of students who have enrolled for French. Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40
We know A U B = A + B - (A n B) i.e, 40 = A + 22 – 12 or
A = 30 which is the set of students who have enrolled for Italian and includes those who have enrolled for both the subjects.
However, we need to find out the number of students who have enrolled for only Italian = Students enrolled for Italian - Students enrolled for both French and Italian = 30 - 12 = 18.
