snhu MODULE TWO PROBLEM SET This document is proprietary to Southern New Hampshire University. It and the problems within may not be posted on any non-SNHU website. Scotty Folker 1
snhu Directions: Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. PROBLEM 1 Part 1. Indicate whether the argument is valid or invalid. For valid arguments, prove that the argument is valid using a truth table. For invalid arguments, give truth values for the variables showing that the argument is not valid. (1) Row 1 2 3 T 4 T 5 6 7 8 p q T T T T F F F T F T F F F F F (pAq) >r : (pvq) >r r pAq T T F T T F F F T F F F T F F p V q T T T T T T F F Hypothesis(p / q) > r T F T T T T T T Conclusion(p V q) > r T F T F T F T T . In rows 4 and 6, the hypothesis is true, but conclusion is false. · Argument is invalid when: p= T, q = F, r = F p = F, q = T, r = F Part 2. Converse and inverse errors are typical forms of invalid argu- ments. Prove that each argument is invalid by giving truth values for the variables showing that the argument is invalid. You may find it eas- ier to find the truth values by constructing a truth table.
snhu (a) Converse error p -> q q .. p p q p > q T T T F F T F T T F F T F p T T F · In row 3, both hypotheses are true, but the conclusion is false. · Argument is invalid when: p = F, q = T (b) Inverse error p -> q p q-p T T T F F T F F F T F F F T T T F T T T · In row 3, both hypotheses are true, but the conclusion is false. · Argument is invalid when: p= F, q = T Part 3. Which of the following arguments are invalid and which are valid? Prove your answer by replacing each proposition with a variable to obtain the form of the argument. Then prove that the form is valid or invalid.