Draw a Venn diagram and use the given information to fill in the number of elements in each region.

Check out the diagram below for the filled in boxes

14 goes in the first box (inside A, but outside B)

7 goes in the overlapping circle regions

5 goes in the third box (inside B, outside A)

3 goes in the box outside of the circles

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Explanation:

means there are 26 items that are in A, B or both.

n(A) = 21 means there are 21 items in A

n(B) = 12 means there are 12 items in B

We don't know the value of which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let

It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.

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So there are 7 items in both regions.

This means there are items that are in set A only. In other words, 14 items are in circle A, but not in circle B.

Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.

Similarly, there are items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.

The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.

Again the diagram is posted below with the filled in values.

x

step-by-step explanation:

i can't solve unless i know what the line is

step-by-step explanation:

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