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Homework 1 Solution
p.5 #1: It is sunny. So I should take off my sunglasses.
p. 6 #3: No one but you has had their hands in the cookie-jar. And the scene of the crime isl ittered with cookie-crumps. You're the culprit!
p.16 A: The following argument is valid (not checking all of them here):
Socrates is a man.
All men are carrots.
$\therefore$ Socrates is a carrot.
comment: Although it is absurd to claim that Socrates (the human) was a carrot, we accept the premises for what they are. Since all men are carrots and Socrates was a man, then he is an example of a carrot according to this argument. There are no counterexamples to refute this argument, so it is valid and not sound (assuming "Socrates" is referring to the ancient Greek human, of course).
The following argument is valid:
Joe is now 19 years old.
Joe is now 87 years old.
$\therefore$ Bob is now 20 years old.
comment: This one is tricky -- the problem here is that the premises contradict each other. This means that it is impossible to come up with a counterexample, so by our definition of validity ("a counterexample does not exist"), it is a valid statement. This is similar to why later define the conditional connective to always yield "true" when it starts with a false.
Arguably, the word "Joe" could refer to two different people, but logic cannot detect that. Since it is exactly the same name, it must be the same individual.
The following arugment is invalid:
If I pull the trigger, Abe Lincoln will die.
I do not pull the trigger.
$\therefore$ Abe Lincoln will not die.
comment: This argument is invalid because a counterexample exists. Consider a case where I do not pull the trigger BUT Abe Lincoln has a heart attack and dies. In this case, the first premise conditional is still "true" (the "if" condition is never met though, so it's irrelevant) and the second premise is true, yet the conclusion is false.