A. For each of the deductive arguments below, do the following. First, reconstruct the argument (i.e., put it into standard form). Second, identify the general structure of the argument (using letters as variables). Third, state whether the argument is valid or invalid. Finally, if the argument is valid, provide a proof to demonstrate this fact; if the argument is invalid describe a counterexample to demonstrate this fact. [Each of the two questions is worth 10 points]

1. Presumably, everyone will agree that the combination is requiredthat is, one thing we know for sure is that we can't open the safe without the combination. But luckily, we already have the combination. So, another thing we know for sure is that we are able to open the safe.

2. There are a couple of different things that would explain why the cookies I made taste so awful. One possibility is that I put way too much salt in the batter; the other is that I added too little sugar. I suppose it's possible that I made both mistakes, but the main point is that I'm confident I made at least one of them. And, when I think about it carefully, I have a distinct memory of adding the correct amount of sugar. I believe, then, that I put too much salt in the batter.

B. For the inductive enthymeme (incompletely stated argument) below, do the following. First, reconstruct the argument, and include any implicit premises (be sure to label any implicit premises). Second, describe evidence that would constitute an undercutting defeater for the argument. Finally, explain why this evidence would constitute an undercutting defeater rather than a rebutting defeater. [This question is worth 10 points]

3. There are five Great Lakes in North America (at least according to the standard division). Three of these lakes (Superior, Michigan, and Huron) were formed due to the movement of a massive glacier at the end of the last ice age. Presumably, then, Lake Ontario was formed in that very same way.