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?

Question

Philoid · Accepted Answer

Let F be the set of people who speak French,

and S be the set of people who speak Spanish.

Number of people who speak French = n(F) = 50

Number of people who speak Spanish = n(S) = 20

Number of people who can both speak French and Spanish

= n(F ∩ S)

= 10

Number of people who speak at least one of these two languages = n(F ∪ S)

We know that-

n(F ∪ S) = n(F) + n(S) - n(F ∩ S)

= 50+20 - 10

= 60

∴ n(H ∩ E) = 60

Thus, 60 people can speak at least one of French or Spanish.