Question

A survey was given to 270 people asking whether people like dogs and/or cats. 124 said they like dogs 156 said they like cats 51 said they don't like cats or dogs. How many said they liked both cats and dogs?

Answer 1

To find the number of people who liked both cats and dogs in the survey, we use the principle of inclusion-exclusion, subtracting those who don't like either from the total, resulting in 61 people who like both.

Step-by-step explanation:

To determine how many people said they liked both cats and dogs from a survey of 270 people, we can use the principle of inclusion-exclusion in set theory. First, we add the number of people who like dogs (124) to the number who like cats (156), which gives us 280. However, this total includes those who like both. Since 51 people do not like either, if we subtract them from the total number of people surveyed (270), we are left with 219 people that like at least one of the two pets. Now, we subtract this number from the 280 to find the number of people who like both, which would be 280 - 219 = 61 people who like both cats and dogs.