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 dog or cat as their pet animal at home?

Answer 1

i. Let U be the set of all the students, then n(U) = 28 

Let D be the set of students who have dog as pet and C be the set of students who have cat as pet. 

10 students have dog and cat as their pet animal n(D ∩ C) = 10

From venn diagram, 

ii. Number of students who have cat or dog as pet 

= n(D ∪ C) 

= 8 + 10 + 6 

= 24 

iii. Number of students who do not have dog or cat as pet = n (U) – n(D ∪ C) = 28 – 24 = 4