Answer:
Let's look at the Venn diagram and the data we have:
There are 12 pupils
9 have a brother
7 have a sister
2 have neither.
Now let's look at the diagram.
We know that the circle B represents the pupils who have a brother
Circle S represents the students that have a sister.
Then the intersection of the circles, represents the number of students that have both.
And the space outside the circles represents the pupils that do not have a brother nor a sister.
Then the first thing we can complete is a 2 in the bottom left corner, because we already know that there are 2 pupils that do not have brothers nor sisters.
Now let's find the number of students that have both, brothers and sisters:
There are 12 pupils.
9 have a brother
7 have a sister
2 have neither
if we add that, we get:
9 + 7 + 2 = 18
This is larger than 12, this means that we are counting some of the students more than once.
If X is the number of students that we are counting twice, we should have:
18 - X = 12
18 -12 = X = 6
There are 6 students who we are counting twice, and this happens because these 6 students have a brother and a sister.
Then in the intersection of both circles we should put a 6.
At the left of that (in the part that we have only circle B) we need to write the number of students that only have a brother, this is the number of students that have a brother minus the number of pupils that have a brother and a sister, this is:
9 - 6 = 3
We need to write a 3 in that square.
And in the last square (the one that is only one circle S) we need to write the number of pupils that only have a sister, this is calculated in the same way than before, this is:
7 - 6 = 1
We need to write a 1 in the rightmost square.
