Question

Analyze the following arguments and tell whether they are valid and sound:

1) 1. If Missy is a cat , then she is a mammal. 2. Missy is not a mammal. 3. Therefore, Missy is not a cat. 2) 1. If Fido is a dog, then he is a mammal.

2. Fido is a dog. 3. Therefore, he is a mammal.

3) 1. If Fido is a dog then he is a mammal. 2. Fido is not a dog. 3. Therefore, Fido is not a mammal.

Answer 1

Note that a => b then we can conclude that ~b => ~a.

1) 1. If Missy is a cat , then she is a mammal. 2. Missy is not a mammal. 3. Therefore, Missy is not a cat. ( Valid by ~b => ~a. )

2) 1. If Fido is a dog, then he is a mammal. 2. Fido is a dog. 3. Therefore, he is a mammal. ( Valid by a => b. )

3) 1. If Fido is a dog then he is a mammal. 2. Fido is not a dog. 3. Therefore, Fido is not a mammal. (Invalid as a => b does not mean ~a => ~b. )