Explain why in the Venn Diagram example the number who liked Hip Hop plus the number who liked Country was NOT the same as the number in the union of the two sets.

Question

Mathematics

Cesar Yang

17 June, 08:28

Explain why in the Venn Diagram example the number who liked Hip Hop plus the number who liked Country was NOT the same as the number in the union of the two sets.

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Jesse Farley · Answer 1

Suppose that you have 50 people that like hip hop and 50 people that like country.

Now, the union of those sets would be 50 + 50 = 100 people, right?

Well, this may be incorrect, because in the 50 people that like hip hop, we may have, for example, 10, that also like country (this means that in the 50 people that like country, we also have 10 that like hip hop).

Then when we are adding 50 + 50 we are counting those 10 people in both groups, and that is why the direct addition may be different than the union of both sets.

In more technical words, the union of two sets is equal to the addition of the elements of both sets minus the elements in the intersection of both sets (in our prior example, the 10 people that like hip hop and country music are the intersection of both sets)