Part 1

1. What are the four connectives in propositional logic, and what do they mean?

2. How do parentheses change the meaning of symbolized statements?

3. What is the rationale behind the short method of argument evaluation?

4. What is the method of proof? How is it used?

5. If a specific argument's form is valid, what does that imply about other arguments using the same form? How does that fact help you evaluate arguments?

Part 2

a. Translate the following arguments into propositional logic. b. Construct a truth table to test the argument. (Please use the Canvas insert table to keep your work clear; the lines will not be visible when you save the exercise, but the information will remain aligned if you center the data.) c. Determine whether the argument is valid or invalid and explain why.

"Either that wallpaper goes or I go!"

Part 3

Use what we have learned about propositional logic to figure out the correct response to the following sci-fi logic puzzle. As you will see, it is similar to the last puzzle, so you can use similar techniques to solve it. Even if you cannot be sure of the final answer, give it a try and post what you come up with. Construct a truth table to determine whether statements are true or false by considering the form of the argument and what truth values you have to test in order to assess their validity. This exercise is in a discussion forum, so, after your first post, you can see what your group members answered and whether your assessment agrees with theirs or not.

On the exoplanet Proxima b, all inhabitants are born as one of two types: they must either tell the truth compulsively or they must lie compulsively. This inherited condition is permanent and has been found to be totally resilient against all the advancements of modern medicine. Unfortunately, there is no way to tell the honest Proxes from the liarsexcept for propositional logic! You are a young space explorer now wayfaring across the planet and are in dire need of accurate directions to the nearest Earth colony. After mucking about in the planet's mountainous terrain for hours in increasing desperation, you come across two Proxes, whom we'll call P and Q. In order to gauge whether you can trust one, both, or neither of the Proxes, you ask P, "Are you both honest?" She replies with a yes or no answer. After considering her answer, you ask P a second question: "Are you two both the same type of Prox?" After P replies, again with a yes or no answer, you know for certain whether P and Q are lying Proxes or honest Proxes. Should you trust P, Q, neither, or both of the Proxes? Why?

(Hint: As you construct your truth table, you will see that there are only four possibilities, and that P's yes or no answers to the two questions eliminate all but one possible identity for the two Proxes.)