Represent the following situation using Venn diagrams and answer the questions that follow.
In a survey of 100 students in the institute language studies at oxford university, the number of
students studying various languages in last four years were found to be : Italian 28, German
30,French 42,Italian and French 10, Italian and German 8, German and French 5, all the three
languages 3. (1 point each)
a. Venn diagram.
b. How many students are studying none of the languages?
c. How many students had French as their only language?
d. How many students are studying at least one of the languages?
All the data is presented very nicely
Draw 3 intersecting circles, label them I, G, and F
enter 3 in the intersection of all the circles
now look at the intersections of 2 at a time
e.g. German and French, G and I , it says 5 take those two
BUT you have already accounted for 3 of those, so place 2 in the
part representing "F and G only"
repeat for the other two pairs
now look at the whole circles, e.g the I circle
notice that 3 parts are already entered, leaving the "Italian Only" part
calculate how many take only Italian.
do this for all the whole circles.
Now all up all the components, that should be ≤ 100
The difference would be the number of students not taking any of
the 3 languages.
You should be able to answer any of the questions.