Question

In a group of $15,7$ have studied German, $8$ have studied French, and $3$ have not studied either. How many of these have studied both German and French?

• A. $0$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (B)

$3$

Since $3$ have neither studied German nor French

$n(G\cup F)=15-3=12$

By set theory

$n(G\cap F)=n\left(G\right)+n\left(F\right)-n(G\cup F)$

$=7+8-12=3$