How many households own no pet

Question

A survey of 50 households finds that 28 own a cat, 22 own a dog, and 12 own both. How many households own neither a cat nor a dog?

Accepted Answer

First count households owning at least one pet with inclusion-exclusion for two sets: 	ext{cat} \cup 	ext{dog} = 28 + 22 - 12 = 38. "Neither" is everyone else, so subtract from the total of 50: 50 - 38 = 12. Takeaway. Count "at least one" first, then "neither" is (total) minus that. Here 50 - (28 + 22 - 12) = 12.

How many households own no pet

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