Question

A group conducted a survey of 100 consumers and reported that 72 consumers like apples and 45 consumers like oranges, what is the least number that must have liked both products?

(a) 14

(b) 15

(c) 16

(d) 17

I have been asked this question in homework.

The doubt is from Practical Problems on Union and Intersection of Two Sets topic in chapter Sets of Mathematics – Class 11

Answer 1

Right choice is (d) 17

The explanation: n(U)=100, n(A)=72, n(O)=45

n (A∪O) = n (A) + n (O) – n(A∩O)

n (A∪O) ≤ n(U) => n (A∪O) ≤ 100

Greatest value of n (A∪O) is 100 which gives least value of n(A∩O)

100=72+45 – n(A∩O)

n(A∩O) = 17 least value of n(A∩O).