For each of the following, please evaluate whether it is valid. If it is valid, then explain briefly why you think so. If it is invalid, then describe a situation in a few sentences that
shows it is invalid -- that is, a situation in which the premises are true and the conclusion is false. Be sure to include enough detail that a reader can tell that the premises are clearly
true, and the conclusion clearly false.
A. Max and Claire are not related, and Nancy is Max's mother. Therefore, Nancy is not Claire's mother.
B. Max and Claire are related, and Nancy is not Max's mother. Therefore, Nancy is not Claire's mother.
C. Either it's raining, or it's snowing. And it's definitely snowing. So, it's not raining.
D. Either it's raining, or it's snowing. And it's too hot for any snow. So, it's raining.
E. All spiders have 2 legs, and all humans have 2 legs. Thus, all humans are spiders.
F. Some vitamins are expensive, and no expensive things are nutritious. Thus, some vitamins are not nutritious.
2. For each of the following, please evaluate whether it is valid. If it is valid, then explain briefly why you think so. If it is invalid, then describe a situation in a few sentences that shows it is invalid -- that is, a situation in which the premises are true and the conclusion is false. Be sure to include enough detail that a reader can tell that the premises are clearly true, and the conclusion clearly false.
A. Max and Claire are not related, and Nancy is Max's mother. Therefore, Nancy is not Claire's mother.
B. Max and Claire are related, and Nancy is not Max's mother. Therefore, Nancy is not Claire's mother.
C. Either it's raining, or it's snowing. And it's definitely snowing. So, it's not raining.
D. Either it's raining, or it's snowing. And it's too hot for any snow. So, it's raining.
E. All spiders have 2 legs, and all humans have 2 legs. Thus, all humans are spiders.
F. Some vitamins are expensive, and no expensive things are nutritious. Thus, some vitamins are not nutritious.