Discussion
In a group of 18 people, 10 read French, 11 read English, while 6 read none of these two. How many of them read both French and English ?
Answer: B
9 people read both French and English.
Of the 18 people, 6 read neither language, so 12 read at least one. By the inclusion-exclusion rule:
\[ \begin{aligned} n(F \cup E) &= n(F) + n(E) - n(F \cap E) \\ 12 &= 10 + 11 - n(F \cap E) \\ n(F \cap E) &= 9 \end{aligned} \]
Check: 1 reads French only, 2 read English only, 9 read both and 6 neither, making 18. 3 is the sum of the 'only' groups, and 6 and 4 do not satisfy the totals.
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