Question

In a group of 15, 7 have studied German, 8 have studies French and 3 have not studied either.
How many of these have studies both German and French?
A) 0
B) 3
C) 4
D) 5​

Answer 1

Answer:

===>3

Step-by-step explanation:

n(U)=15

n(German)=7=n(G)

n(French)=8=n(F)

n(students who have studied neither) =3

n(G∪F)=n(U)− n(students who studied neither) =15−3=12

n(G∪F)=n(G)+n(F)−n(G∩F)

12=7+8−n(G∩F)

n(G∩F)=15−12=3

Answer 2

Answer:

B) 3

Step-by-step explanation:

The number who have studied at least one of them is 15 - 3 = 12.

Counted another way, the number who have studied at least one of them

  =  (no. who studied French) + (no. who studied German) - (no. who studied both, since these have so far been counted twice)

  =  8 + 7 - x

  =  15 - x

where x is the number who have studied both (what we want!).

Putting these two things together gives

   15 - x = 12  ⇒  x = 3

Hope this helps.