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. Vivian Nguyen 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) (pAq) >r : (p Vg) >r p q r (p Aq) T T T T T F T F F T F T F F F F T F T F F T F T F T T F F F F F (p V q) (pg) >r) T T T F T T T T T T T T F T F T (p Vg) >r) T F T F T F T T In row 4 and row 6, the premise is TRUE but the conclusion is FALSE. Hence the argument is INVALID
snhu 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. (a) Converse error p > q q .. p p q p -> q T T T F F T F F T F T T In the third row, the premises are all TRUE, but the conclusion is FALSE. Hence, the argument is INVALID. (b) Inverse error p -> q p q p -> q T T T F F T F F T F F T T T bL F F T F T T In the third row, the conclusion is FALSE, while the premise is TRUE. Hence the argument is INVALID.