n(ξ) = 20, n(A) = 8, n(B) = 7, n(A ∩ B) = 0, find n((A ∪ B)′)

Step by step

The question

Question: n(ξ) = 20, n(A) = 8, n(B) = 7, n(A ∩ B) = 0.

Find n((A ∪ B)′).

n of A means how many are in A.

A ∩ B means in both.

(A ∪ B)′ means in neither.

1 Draw the Venn diagram

0 are in both: they go in the middle first.

2 Fill the circles

In A: 8 in all, 0 of them are in the middle.

8 minus 0 is 8.

Careful!

The 0 in the middle are inside both circles.

Taking away 8 and 7 takes them away twice.

In B: 7 minus 0 is 7.

3 Find the outside

The circles hold 8 plus 0 plus 7: 15.

The rest of the 20 are outside: 5.

4 Check

Let's check: the four parts add up to 20.

So it fits!

Let's look back.

First: draw the Venn diagram.

Then: fill the circles.

Then: find the outside.

Last: check.