Question

In a family of 10 members, 7 of them like tea or coffee, 4 of them like tea and 5 of them like coffee. How many of them like neither tea nor coffee?

(a) 1

(b) 2

(c) 3

(d) 4

I have been asked this question in homework.

This intriguing question originated from Practical Problems on Union and Intersection of Two Sets topic in section Sets of Mathematics – Class 11

Answer 1

Correct choice is (c) 3

For explanation I would say: Given, n (T ∪ C) = 7.

By de Morgan’s law, n (T’ ∩ C’) = n (T ∪ C)’ = Total – n (T ∪ C) = 10 – 7 = 3.

So, 3 members like neither tea nor coffee.