Question

Ina committee, 50 people speak French, 20 speak Spanish and 10 speakboth Spanish and French. How many speak at least one of these twolanguages?

Answer 1

LetF be the set of people in the committee who speak French, and

Sbe the set of people in the committee who speak Spanish

∴ n(F)= 50, n(S)= 20, n(S∩F) = 10

Weknow that:

n(S∪F) = n(S)+ n(F)– n(S∩F)

=20 + 50 – 10

=70 – 10 = 60

Thus,60 people in the committee speak at least one of the two languages.