SOLUTION: In a committee of 30 members, 20 speak English and 15 speak French. If 8 speak both languages, how many speak: a) Neither language? b) At least language? c) Only one language?

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Question 1206819: In a committee of 30 members, 20 speak English and 15 speak French. If 8 speak both languages, how many speak:
a) Neither language?
b) At least language?
c) Only one language?
Answer by mananth(16946) About Me  (Show Source):
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In a committee of 30 members, 20 speak English and 15 speak French. If 8 speak both languages, how many speak:
a) Neither language?
b) At least language?
c) Only one language?
u= 30
n(E)=20
n(F) = 15
n(E intersection F )= 8
x = speak neither
n(E)+n(F)-n(E intersection F )+x= 30
20+15-8+x=30
x+27=30
x=3
a) Neither language?
3
b) At least language?
12+8+7=27
c) Only one language?
12+7=19
.