Consider the following argument and its truth table: (pAq) → (p V ¬g) ...p + q |(p^q) → (p V -q) T F F F F F F T F Is the argument valid or invalid? What is the reason? Valid, because some conclusions are true. O Valid, because most hypothesis are true. O Invalid, because all critical rows are false. O Valid, because the conclusion is always true when all hypothesis are true.

Consider the domain of people and the following argument: Hypothesis: If a person is a mathematician, then he/she is a programmer. If a person is a programmer, then he/she is prone to headaches. Conclusion: Therefore, if a person is a mathematician, then he/she is prone to headaches. a. Assign letters to the basic propositions and write each hypothesis and the conclusion as an implication. ● Hint: Use the syntax P(X) : “X > 0” or P(X) : “subject and predicate" to represent your statements. b. Prove the correctness of you answer to item a. by using the logical equivalencies and/or rules of inferences tables from your text which are also available below.

There are fallacies associated with conditional statements. The three most common are Fallacy of the Converse, Fallacy of the Inverse, and Misuse of Hypothetical Syllogism (see link below!). Pick one of these and create an argument to show why it is incorrect.

(b) What is the truth value of ~ (p V q) - r?