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?

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

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