Step by step
The question
Question: 30 people: 18 like tea, 15 like coffee, 7 like both.
How many like neither?
1 Draw the Venn diagram
The box holds all 30 people.
One circle for tea.
One circle for coffee.
The middle is both.
7 like both: they go in the middle first.
2 Fill the circles
Like tea: 18 in all, 7 of them are in the middle.
18 minus 7 is 11.
like only tea = 18 − 7 = 11
Careful!
The 7 in the middle are inside both circles.
If we just take 18 and 15 from 30, the 7 in the middle are taken away twice.
Careful: not 30 − 18 − 15 = −3 ✗
Like coffee: 15 minus 7 is 8.
like only coffee = 15 − 7 = 8
3 Find the outside
The circles hold 11 plus 7 plus 8: 26.
The rest are outside: 30 minus 26 is 4.
neither = 30 − (11 + 7 + 8) = 4
4 Check
Let's check: the four parts add up to 30.
So it fits!
11 + 7 + 8 + 4 = 30
Let's look back.
First: draw the Venn diagram.
Then: fill the circles.
Then: find the outside.
Last: check.
Answer
neither = 30 − (11 + 7 + 8) = 4