show a venn diagram

Question

use a Venn diagram like the one below.

A survey of 134 pet owners yielded the following information: 49 pet owners own fish; 57 own a bird; 50 own a cat; 68 own a dog; 2 own all four; 11 own only fish; 14 own only a bird; 10 own fish and a bird; 21 own fish and a cat; 24 own a bird and a dog; 27 own a cat and a dog; 3 own fish, a bird, a cat, and no dog; 1 owns fish, a bird, a dog, and no cat; 9 own fish, a cat, a dog, and no bird; and 10 own a bird, a cat, a dog, and no fish. How many of the surveyed pet owners have no fish, no birds, no cats, and no dogs?

Answer 1

10 own fish and cat.

If that means fish and cat ONLY (no dog, no bird)

then fish and cat only must be 13 which contradicts the

given figure of 21 no matter how you slice it.

If that means fish and cat with the possibility of dog or bird, then

fish and bird only is 4, which forces cat and fish only to be 19

which contradicts the given figure of 21 no matter how you slice it.

I copied the given data into the venn diagram and crossed them off as I used them.

x is fish and bird ONLY

y is bird and DOG only

z is fish and cat ONLY

lambda is dog and cat ONLY

w is dog only

v is cat only

Here are the five equations:

x + z + 26 = 49 ---> x+z = 23

x +y + 30 = 57 ---> x+y = 27

z + y + lambda + 24 = 50 ---> z + y + lambda = 26

lambda + w + v + 22 = 68 ---> lambda + w + v = 46

x + y + z + 50 = 106 ---> x + y + z = 56

The following statements are UNCLEAR:

10 own fish and a bird; 21 own fish and a cat; 24 own a bird and a dog; 27 own a cat and a dog;

The other statements are unclear.

They are causing problems and create contradictions no matter how they are interpreted.

Please clarify the statement of the problem and repost.

The name of the file is BAD VENN DIAGRAM.jpg