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Test Your Logical Thinking

Here are detailed answers for the Test Your Logical Thinking puzzle:

Premises	Conclusion	Explanation
All men are mortal. Socrates is mortal.	Socrates is a man.	The conclusion does not follow. This argument commits the fallacy of the undistributed middle. Informally speaking, the premises don't make the connection from "Socrates" to "man." Consider the following argument: All men are mortal. My dog Socrates is mortal. Therefore Socrates is a man.
Either you are in New York or you are in Philadelphia. You are not in New York.	You are in Philadelphia.	The conclusion does follow, if we accept the premises as true.
Some dogs are friendly. All dogs are animals.	Some animals are friendly.	The conclusion does follow.
If you won the lottery, you are a millionaire. You are a millionaire.	You won the lottery.	The conclusion does not follow; you could have made your millions some other way. This argument commits the fallacy of affirming the consequent.
No ducks are mammals. No birds are mammals.	Some ducks are not birds.	The conclusion does not follow. If a categorical syllogism contains two negative premises, nothing can be concluded. This argument commits the fallacy of exclusive premises. Even just thinking informally, it's easy to see how you could accept both premises but reject the conclusion.
All humans are mammals. Humans do not have four legs.	Some mammals do not have four legs.	The conclusion follows.
Whenever Drug Y is administered, the patient gets better. Whenever Drug Y is not administered, the patient does not get better.	Drug Y causes the patient to get better.	While it's quite likely that the conclusion is true, it does not follow from the premises, which is what the question asks. It's possible that, for example, Drug Y is only administered to patients who appear likely to get better, or Drug Y is only administered to mitigate the side effects from Wonder Drug X, etc; it's not necessarily true that Drug Y causes the recovery. This argument commits the fallacy of post hoc ergo propter hoc.
If you hit the brakes hard, your car will be rear-ended by the car behind you. If you do not hit the brakes hard, you will hit a child in front of you.	Either you will hit the child or you will be hit by the car behind you.	The conclusion follows. Either you will hit the brakes hard or you won't. Either way, at least one of the two occurrences mentioned in the conclusion will happen.
Whenever you are in Trenton, you are in New Jersey. You are in New Jersey.	You are in Trenton.	The conclusion does not follow. This is another example of affirming the consequent.
Smithville is around 50 kilometres due north of Jonesborough. Jonesborough is around 50 kilometres due north of Browntown.	Browntown is closer to Jonesborough than Smithville.	This conclusion follows. Drawing a diagram may help here.

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If you are interested in other logical-thinking puzzles, you may also want to try Test Your Logical Thinking #2 and Wason's Four-Card Task.