Question

in a survey of 84 pet owners, 29 said they own a dog, and 61 said they own a cat. 27 said they own both a dog and a cat. how many owned neither a cat nor a dog? answer = owners question help: video 1 video 2

Explanation:

Step1: Use the inclusion - exclusion principle

Let \(A\) be the set of dog - owners and \(B\) be the set of cat - owners. The number of people who own either a dog or a cat is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, \(n(A) = 29\), \(n(B)=61\), and \(n(A\cap B)=27\).
So, \(n(A\cup B)=29 + 61-27\).

Step2: Calculate \(n(A\cup B)\)

\(n(A\cup B)=29+61 - 27=63\).

Step3: Find the number of people who own neither

The total number of pet - owners is \(N = 84\). The number of people who own neither a cat nor a dog is \(84−n(A\cup B)\).
So, it is \(84 - 63=21\).

Answer:

21