Venn diagram

University students chose a foreign language for the 1st year. Of the 120 enrolled students, 75 chose English, 65 German, and 40 both English and German. Using the Venn diagram, determine:
- how many of the enrolled students chose English only
- how many of the enrolled students chose only German
- How many of the enrolled students chose English or German
- How many of the enrolled students chose neither English nor German

Correct result:

a =  35
n =  25
c =  100
d =  20

Solution:

$$\begin{gathered} p=40 \\ a=75-p=75-40=35 \end{gathered}$$

$n=65-p=65-40=25$

$c=a+n+p=35+25+40=100$

$d=120-c=120-100=20$

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