Step by step
The question
Question: 25 people: 12 like tea, 10 like coffee, 4 like both.
How many like neither?
1 Draw the Venn diagram
4 like both: they go in the middle first.
2 Fill the circles
Like tea: 12 in all, 4 of them are in the middle.
12 minus 4 is 8.
like only tea = 12 − 4 = 8
Careful!
The 4 in the middle are inside both circles.
Taking away 12 and 10 takes them away twice.
Careful: not 25 − 12 − 10 = 3 ✗
Like coffee: 10 minus 4 is 6.
like only coffee = 10 − 4 = 6
3 Find the outside
The circles hold 8 plus 4 plus 6: 18.
The rest of the 25 are outside: 7.
neither = 25 − (8 + 4 + 6) = 7
4 Check
Let's check: the four parts add up to 25.
So it fits!
8 + 4 + 6 + 7 = 25
Let's look back.
First: draw the Venn diagram.
Then: fill the circles.
Then: find the outside.
Last: check.
Answer
neither = 25 − (8 + 4 + 6) = 7