What does it mean for a sentence to be truth-functional? Why is this important for propositional logic? Give an example of a sentence that is not truth functional.

Week 3 Study Guide
Answer the following seven questions about the reading and videos for the week. Write out your answers on a computer and then either upload the file or paste into the submission text box. Do not write directly into the text box because it doesn’t save your work. If you upload a file, only use doc, docx, pdf, or jpg.

1. For each of the five main logical operators: list the operator, identify it symbol, use the operator in a sentence. It can be hard to use logical operators online. The easiest way is to copy and paste from this list: (• v ⊃ ≡ -). If that doesn’t work, you can simply draw them out on paper and upload a photo along with the assignment.

2. Translate the following English sentences into formal language. Use the suggested constants to stand for the atomic propositions.
a. Either Bob will mop or Tom will mop. (B = Bob will mop; T = Tom will mop)
b. It is not the case that Bob is a burglar. (B = Bob is a burglar)
c. Either it will not rain on Monday or it will not rain on Tuesday. (M = It will rain on Monday; T = It will rain on Tuesday)
d. Tom does not like cheesecake. (T = Tom likes cheesecake)
e. Bob would like to have both a large cat and a small dog as a pet. (C = Bob would like to have a large cat as a pet; D = Bob would like to have a small dog as a pet)
f. Bob Saget is not actually very funny. (B = Bob Saget is very funny)

3. What does it mean for a sentence to be truth-functional? Why is this important for propositional logic? Give an example of a sentence that is not truth functional.

4. Use truth tables to show whether the following inferences are valid. It can be hard to format truth tables online. The easiest way is to make a table in your word processor. If that doesn’t work, you can simply draw out your answers on paper and upload a photo along with the assignment.

5. Is the following sentence true or false: “Kanye West is a frog; therefore, Kanye is married to Kendrick Lamar”? Translate this sentence into logic and then use a truth table to show your reasoning. What does this tell us about the truth of conditional statements?

6. What are the five valid argument forms discussed in 4.2? Give an example of each.

7. Do you find this type of formal logic interesting? Why or why not?

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