Sets to solve the problems

Question

Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 own a dog, and 5 own both a cat and a dog. How many of the students surveyed own neither a cat nor a dog?

Answer 1

The way the question is written, students can be divided into 4 groups:

1) Own a cat (can also own a dog, but don't need to) -- 8

2) Own a dog (can also own a cat, but don't need to) --15

3) Own both a dog and a cat -- 5

4) Own neither a dog nor a cat -- ??

 

Right now, we have students who are double counted.  For example, students who only both a cat and a dog are included in the number of students who own a cat.  Therefore, we need to find the number of students who own only a cat and only a dog.  To do so, you subtract the number of students who own both a cat and a dog (5) from the number of students who own a cat (8) or own a dog (15).

 

8 - 5 = 3 students own only a cat

15 - 5 = 10 students own only a dog

 

5 students own both a cat and a dog. 

 

Now, no students are double counted.

 

We know that there are 30 students total.  If we add up the number of students who own only a cat, only a dog and both a cat and a dog, we get 3 + 10 + 5 = 18 students. 

 

Thus, the number of students who own neither a cat nor a dog is:

30 - 18 = 12 students