Question

100 students were interviewed. 28 took Physical Education, 31 took Biology, 42 to English, 9 took Physical Education and Biology, 10 took Physical Education and English and 6 took Biology and English.

i. How many students took none of the three subjects
ii. How many took physical education, but not Biology or English
iii. how many students took biology and Physical education but not English

Answer 1

Answer:

no subject = 24

only physical Education = 9

Step-by-step explanation:

Physical Education P = 28

Biology B = 31

English E = 42

P ∩ B  = 9

P ∩ E  = 10

E ∩ B  = 6

Assuming no one took all three subjects P ∩ B ∩ E = 0

Total = 100

Total = P + B + E - P ∩ B - P ∩ E - E ∩ B + P ∩ B ∩ E + no subject

=> 100 = 28 + 31 + 42 - 9 - 10 - 6 + 0 + no subject

=> no subject = 24

only physical Education = P - P ∩ B - P ∩ E +  P ∩ B ∩ E = 28 - 9 - 10  + 0

= 9

biology and Physical education but not english = P ∩ B - P ∩ B ∩ E = 9