Answer to Question #111971 in Discrete Mathematics for onyi

Question

3. Stella Maris Schools, at one time, has 37 vacancies for teachers, out of which 22 are for English Language, 20 for History, 17 for Fine-Art. Of these vacancies, 11 are for both English Language and History, 8 for both, History and Fine Art, 7 for English Language and Fine-Art.
Using a Venn diagram or otherwise, find the number of teachers who must be able to teach:
a. All the three subjects.
b. Fine Art only
c. English Language and History not Fine Art.

Answer 1

Answer:(a) 4 ; (b) 6 ; (c) 7.(a) (22+20+17) - (11+8+7) + number of teacher able to teach all subjects = 37number of teacher able to teach all subjects = 37 - 59 + 26 = 4(b) Fine Art only  = Fine Art - (Fine Art and History) - (Fine Art and English) + (All three) = 17 - 8 - 7 + 4 = 6(c) English Language and History not Fine Art = (English and History) - (All three) = 11 - 4 =7