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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?
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?
CBSE | Class 11 | Exercise 1.6 | Maths | NCERT | Sets
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’s consider as the set of people in the committee who speak French as F, and
the set of people in the committee who speak Spanish as S.

$n\left( F \right)\text{ }=\text{ }50$

$n\left( S \right)\text{ }=\text{ }20$

$n(S~\cap ~F)\text{ }=\text{ }10$

This can be written as

$n(S~\cup ~F)\text{ }=~n\left( S \right)\text{ }+~n\left( F \right)-n(S~\cap ~F)$

Now, substitute the values

$n(S~\cup ~F)\text{ }=\text{ }20\text{ }+\text{ }50-10$

Calculating further

$n(S~\cup ~F)\text{ }=\text{ }70-10$

$n(S~\cup ~F)\text{ }=\text{ }60$

As a result, in the committee 60 people speak at least one of the two languages.

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