Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey.results of the survey indicated that 8 students own a cat, 15 students own a dog and five students owned neither a cat or a dog. how many of the students surveyed owned neither a cat nor a dog.

five students owned neither a cat or a dog

To find out how many students owned neither a cat nor a dog, we need to use the concept of sets and apply the principle of inclusion-exclusion.

Let's break it down step by step:

1. Start with the total number of students surveyed, which is 30.

2. Out of these 30 students, 8 own a cat and 15 own a dog.

3. We know that 5 students owned neither a cat nor a dog.

4. Now, to find the number of students who owned either a cat or a dog, we need to add the number of cat owners (8) and the number of dog owners (15) together: 8 + 15 = 23.

5. However, this count includes the students who own both a cat and a dog. To exclude the students with both pets, we need to subtract them from the total.

6. To do that, we will subtract the number of students who own both a cat and a dog from the count in step 4. Unfortunately, we don't know the exact number of students who own both pets, but we can find it by subtracting the number of students who do not own any pets from the count in step 3, which is 5: 23 - 5 = 18.

7. So, out of the 30 students surveyed, 18 owned either a cat or a dog (or both).

8. Finally, to find the number of students who owned neither a cat nor a dog, we need to subtract the count in step 7 from the total number of students surveyed: 30 - 18 = 12.

Therefore, 12 students surveyed owned neither a cat nor a dog.