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Validity of Arguments and Logical Errors in Discrete Mathematics

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.