A veterinarian has 70 clients who own cats, dogs, or both. Of these clients, 36 own cats, including 20 clients who own both cats and dogs. Which of the following statements must be true? Indicate all such statements.

Question

Alayna

Mathematics

4 July, 11:21

A veterinarian has 70 clients who own cats, dogs, or both. Of these clients, 36 own cats, including 20 clients who own both cats and dogs. Which of the following statements must be true? Indicate all such statements.

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Answers (1)

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Enrique Horton · Answer 1

The three statements are true.

Step-by-step explanation:

The question is incomplete:

A veterinarian has 70 clients who own cats, dogs, or both. Of these clients, 36 own cats, including 20 clients who own both cats and dogs. Which of the following statements must be true? Indicate all such statements.

A. There are 54 clients who own dogs.

B. There are 34 clients who own dogs but not cats.

C. There are 16 clients who own cats but not dogs.

A. There are 54 clients who own dogs.

TRUE. Of the 70 clients, only 36 own cats. There are left 34 clients that own only dogs. If we add the 20 clients that own both cats and dogs, we have 34+20=54 clients who own dogs.

B. There are 34 clients who own dogs but not cats.

TRUE. Of the 70 clients, only 36 own cats. Then, there are left 70-36=34 clients that own only dogs.

C. There are 16 clients who own cats but not dogs.

TRUE. Out of the 36 clients that own cats (only of with dogs), there are 20 that own both. Therefore, there are 36-20=16 clients that own only cats.