Step by step
The question
Question: 30 students: 18 play football, 15 play tennis, 8 play both.
How many play neither?
1 Draw the Venn diagram
8 play both: they go in the middle first.
2 Fill the circles
Play football: 18 in all, 8 of them are in the middle.
18 minus 8 is 10.
play only football = 18 − 8 = 10
Careful!
The 8 in the middle are inside both circles.
Taking away 18 and 15 takes them away twice.
Careful: not 30 − 18 − 15 = −3 ✗
Play tennis: 15 minus 8 is 7.
play only tennis = 15 − 8 = 7
3 Find the outside
The circles hold 10 plus 8 plus 7: 25.
The rest of the 30 are outside: 5.
neither = 30 − (10 + 8 + 7) = 5
4 Check
Let's check: the four parts add up to 30.
So it fits!
10 + 8 + 7 + 5 = 30
Let's look back.
First: draw the Venn diagram.
Then: fill the circles.
Then: find the outside.
Last: check.
Answer
neither = 30 − (10 + 8 + 7) = 5