math - how to interpret multiple venn diagram -

could 1 explain logic behind multiple venn diagram explaining these numbers represent in picture. thanx in advance.

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the number in each location represents number of items can there , else.

for example there 1 item both s , r , not in e or r.

there 2 items in s, r, , e , not in r.

there 3 items in e , r , not in s or r.

four items in r , else

etc.

conveniently enough, because of categories mutually exclusive, can find number of items in arbitrary category adding sub-categories make up.

for example, number of items in s , r total 1+9+2+8 = 20

Sharma