Question

in a survey of 21 students, 14 students said they own a dog, 10 said they own a cat, and 6 said they own a bird. of these students, 5 own both a dog and a cat, 3 own both a dog and a bird, and 4 own both a cat and a bird. if none of the students surveyed own all three pets, which of the following venn - diagrams correctly and completely represents all the information about the students surveyed?

Explanation:

Step1: Analyze given data

We have 14 dog - owners, 10 cat - owners, 6 bird - owners, 5 own both dog and cat, 3 own both dog and bird, 4 own both cat and bird, and 0 own all three.

Step2: Check intersection values in Venn - diagrams

In a Venn - diagram for three sets (dogs, cats, birds), the intersection of dog and cat should have 5, dog and bird should have 3, cat and bird should have 4, and the intersection of all three should have 0.

Step3: Match with options

By checking each Venn - diagram option against the above intersection values, we can find the correct one.

Answer:

(Without seeing the actual options clearly labeled, we can't give a specific option. But the correct Venn - diagram will have the intersection of the dog and cat circles with 5 elements, the intersection of the dog and bird circles with 3 elements, the intersection of the cat and bird circles with 4 elements, and the intersection of all three circles with 0 elements.)