Question

In a class, 8 students out of 28 have a dog as their pet animal at home, 6 students have a cat as their pet animal. 10 students have dog and cat both, then how many students do not have a dog or cat as their pet animal at home?

Answer 1

Let U be the universe of students in a class, D is the set of dog keepers, and C is the set of students who keep cats.

We have, 

Total number of students = 28; 

n (U) = 28

n (D) = n (dog only) + n (dog and cat)

= 8 + 10 = 18

n (C) = n (Cat only) + n (dog and cat)

= 6 + 10 = 16

n (D ∪ C) = n (D) + n (C) - n (D ∩ C)

= 18 + 16 - 10 

= 34 - 10

= 24 

Students who do not have a pet 

= n (U) - n (D ∪ C)

= 28 - 24

= 4

So, the number of students that do not have a dog or a cat as their pet is 4.