A vet surveys 26 of his patrons. He discovers that 14 have dogs. 10 have cats. 5 have fish. 4 have dogs & cats. 3 have dogs & fish. 1 has a cat & a fish. Use a diagram to answer the following question: If no one has all 3 kinds of pets, how many patrons have none of these pets?

Answer 1

make 3 overlapping circles, label them D, C, and F

4 have dogs and cats, put 4 in the region overlapped by D andC but not F
3 have dogs and fish, put 3 in the region overlapping D and F, but not C
1 has a cat and a fish, put 1 in the region overlapping C and F, but not D

Now look at circle D, we already have a total of 7 in there, but there were 14 that have dogs. So the region of D not overlapping anything is 7
Same way, 5 into rest of C, 1 into rest of F

Add them all up, I get 21
But there were 26 patrons, so 5 did not have any of the 3 kinds of pets

Answer 2

5 didn't

Answer 3

I HATE MATH

Answer 4

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