In a class of 30 students, 18 study French (F) and 14 study Spanish (S). Every student studies at least one language. How many students study BOTH French and Spanish?

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Question

In a class of 30 students, 18 study French (F) and 14 study Spanish (S). Every student studies at least one language. How many students study BOTH French and Spanish?

Accepted Answer

2 — Using n(F ∪ S) = n(F) + n(S) − n(F ∩ S): 30 = 18 + 14 − n(F ∩ S), so n(F ∩ S) = 32 − 30 = 2. A common error is to add the sets and subtract the total rather than rearranging correctly.

Answer

2

Answer

4

Answer

8

Answer

32

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