In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Solution:

Let F be the set of people in the committee who speak French, and S be the set of people in the committee who speak Spanish.

It is given that in a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French.

Therefore,

n (F) = 50, n (S) = 20 and n (S ∩ F) = 10

We know that n(S υ F) is,

n (S υ F) = n (S) + n (F) - n (S ∩ F)

= 50 + 20 - 10

= 70 - 10

= 60

Hence, 60 people in the committee speak at least one of the two languages

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 8

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Summary:

It is given that in a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. We have found that 60 people in the committee speak at least one of these two languages.