88. A Class Adviser Surveys 35 Of His Students On The Kind Of Pets They Have At Home,, Found That 15 Have Dogs, 12 Have Cats, And 8 Have Birds. Five H

88. A class adviser surveys 35 of his students on the kind of pets they have at home,

found that 15 have dogs, 12 have cats, and 8 have birds. Five have dogs and cats,
4 have dogs and birds, and 2 have cats and birds. If no one has all three kinds of pets.
how many students have none of these pets?

thnx for the answer  

Answer: 11 students

Step-by-step explanation:

In this union and intersection, we use the formula n(A u B u C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩C) + n (A ∩ B  ∩ C)

Substituting the given, we have

15 + 12 + 8 - 5 - 4 - 2 + 0 = 24

Since we have 35 students, we subtract 24 from the # of students

35 - 24 = 11

And that gives us 11 students who have none of these pets.