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

The correct option is B $3$

$n\left(U\right)=15$

$n\left(German\right)=7=n\left(G\right)$

$n\left(French\right)=8=n\left(F\right)$

n(students who have studied neither) $=3$

$n(G\cup F)=n\left(U\right)-$ n(students who studied neither) $=15-3=12$

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

$12=7+8-n(G\cap F)$

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