Q. 445.0( 3 Votes )

#
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?

Answer :

Let F denote the set of people who speak French and S denote the set of people who speak Spanish. Then F ∪ S denote the people who like to speak at least one of these two languages and F ∩ S denote the people who like to speak both Spanish and French.

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

Method 1:

We know,

n(F ∪ S) = n( F ) + n(S) - n(F ∩ S)

n(F ∪ S) = 50 + 20 - 10

.

^{.}. n(F ∪ S) = 60

Therefore, 60 people like to speak at least one of these two languages.

Method 2:

Let n(F ∪ S) = x

From the diagram we get

n(F ∪ S) = 40 + 10 + 10

.^{.}. n(F ∪ S) = 60

Therefore, 60 people like to speak at least one of these two languages

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Interactive Quiz on Sets33 mins

Sets and Wavy Curve Methods - 0149 mins

Interactive Quiz :Sets and Wavy Curve Methods - 0663 mins

Sets and Wavy Curve Methods - 0465 mins

Sets and Wavy Curve Methods - 0958 mins

Sets and Wavy Curve Methods - 0850 mins

Sets and Wavy Curve Methods - 0754 mins

Sets and Wavy Curve Methods - 0354 mins

Sets and Wavy Curve Methods - 0565 mins

Sets and Wavy Curve Methods - 1252 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation