NCERT Class XI Mathematics - Sets - Solutions
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Question : 57
Total: 73
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 who speak French and S be the set of people who speak Spanish.
Here n(F) = 50, n(S) = 20 and n(F ∩ S) = 10
We know that
n(F ∪ S) = n(F) + n(S) – n(F ∩ S)
∴ n(F ∪ S) = 50 + 20 – 10 = 60
∴ Number of people who speak at least one of these two languages = 60.
Here n(F) = 50, n(S) = 20 and n(F ∩ S) = 10
We know that
n(F ∪ S) = n(F) + n(S) – n(F ∩ S)
∴ n(F ∪ S) = 50 + 20 – 10 = 60
∴ Number of people who speak at least one of these two languages = 60.
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