Step by step
The question
Question: 35 people: 20 read books, 18 read comics, 10 read both.
How many read neither?
1 Draw the Venn diagram
10 read both: they go in the middle first.
2 Fill the circles
Read books: 20 in all, 10 of them are in the middle.
20 minus 10 is 10.
read only books = 20 − 10 = 10
Careful!
The 10 in the middle are inside both circles.
Taking away 20 and 18 takes them away twice.
Careful: not 35 − 20 − 18 = −3 ✗
Read comics: 18 minus 10 is 8.
read only comics = 18 − 10 = 8
3 Find the outside
The circles hold 10 plus 10 plus 8: 28.
The rest of the 35 are outside: 7.
neither = 35 − (10 + 10 + 8) = 7
4 Check
Let's check: the four parts add up to 35.
So it fits!
10 + 10 + 8 + 7 = 35
Let's look back.
First: draw the Venn diagram.
Then: fill the circles.
Then: find the outside.
Last: check.
Answer
neither = 35 − (10 + 10 + 8) = 7