Question

in a survey of 74 pet owners, 26 said they own a dog, and 40 said they own a cat. missing number of owners who own both a dog and a cat said they own both a dog and a cat. how many owned neither a cat nor a dog? answer = owners

Explanation:

Step1: Use the inclusion - exclusion principle

Let \(A\) be the set of dog - owners and \(B\) be the set of cat - owners. The formula for \(|A\cup B|\) is \(|A|+|B|-|A\cap B|\). Here, \(|A| = 26\), \(|B| = 40\), and \(|A\cap B|=14\). So \(|A\cup B|=26 + 40-14\).

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

\(26+40 - 14=52\).

Step3: Find the number of owners who own neither

The total number of pet - owners is \(N = 74\). The number of owners who own neither a cat nor a dog is \(74-|A\cup B|\). So it is \(74 - 52\).

Step4: Calculate the final result

\(74-52 = 22\).

Answer:

22