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. Jamar Sampson 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) (p /q) >r : (pvq) >r Looking at a created truth table, the last two columns are not equal. That makes this argument invalid. 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 If the truth value of p is False while the value of q is True, then p -> qqbothcanbedeterminedtobeTrue, whilepis False. Since the premise is False and the consequent is True, by implication, this eval- uates to True. (b) Inverse error p > q ?.q Based on the values of the created truth table, the values of p are false. Therefore the argument is invalid.
snhu 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. (a) The patient has high blood pressure or diabetes or both. The patient has diabetes or high cholesterol or both. .. The patient has high blood pressure or high cholesterol. P = Patients with high blood pressure. Q = Patients with diabetes. R = Patients with high cholesterol. 1. patients with diabetes, high blood pressure, or both, to be represented by (P VQ). 2. Patients with diabetes, cholesterol, or both, to be represented by (Q VR). 3. The conclusion statement could be viewed as ( PVQVR).Theconclusionlistedshowsas(PV R). 4. This concludes that the final statement is false.