Question

in a survey of 177 pet owners, 85 said they own a dog, and 69 said they own a cat. 19 said they own both a dog and a cat. how many owned a dog but not a cat? answer = owners question help: video

Explanation:

Step1: Identify relevant numbers

Let the number of dog - owners be $n(D)=85$, and the number of owners of both dog and cat be $n(D\cap C)=19$.

Step2: Calculate number of dog - only owners

We want to find the number of people who own a dog but not a cat, which is $n(D\cap\overline{C})$. We know that $n(D)=n(D\cap C)+n(D\cap\overline{C})$. So, $n(D\cap\overline{C})=n(D)-n(D\cap C)$.
Substitute the values: $n(D\cap\overline{C}) = 85 - 19$.
$n(D\cap\overline{C})=66$.

Answer:

66