With Dogs only: 15 - (5+4) = 6
With Cats only: 12 - (5+2) = 5
With Birds only: 8 - (4+2) = 2
With dogs and cats: 5
With birds and dogs: 4
With cats and birds: 2
With dogs, cats, and birds : 0
Total students surveyed: 35
6 + 5 + 2 + 5 + 4 + 2 = 24 students with pets
35 - 24 = 11 students have no pets