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At my office, 16 people own cats, 11 people own dogs, and 7 people own both cats and dogs. How many people own a cat or a dog?

(Remember that in mathematics, the word "or" is used in the inclusive sense. So if you own both a cat and a dog, then you are included in the category of people "who own a cat or a dog".)

 Jun 30, 2021
 #1
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By the principle of inclusion-exclusion(see here: https://brilliant.org/wiki/principle-of-inclusion-and-exclusion-pie/) We have that the answer to be $16 + 11 - 7 = 20$

 Jun 30, 2021
 #2
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Just use a Venn diagram of 2 overlapping circles.

 

One circle is dogs the other is cats the overlapping is both.

so 7 goes in the overlap

 

so how many go in the other two bits?

 

You work it out.  It really is not hard.

 Jun 30, 2021

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