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# Logic I, Week 5, Class 09/15 PHL 1100

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This 5 page Class Notes was uploaded by Amanda Notetaker on Sunday September 18, 2016. The Class Notes belongs to PHL 1100 at Appalachian State University taught by Dr. Patrick Rardin in Fall 2016. Since its upload, it has received 5 views. For similar materials see Logic I in Philosophy at Appalachian State University.

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Date Created: 09/18/16

Logic I Week 5 09/15 Homework 8 Answers Pg 322 B 3. P1 P2 ∴ E F E ⊃ F F ⊃ E E ∨ F T T T T T T F F T T F T T F T F F T T F Invalid 4. P1 P2 ∴ G H G ∨ H G ⋅ H (G ∨ H) ⊃ (G ⋅ H) ~(G ⋅ H) ~(G ∨ H) T T T T T F F T F T F F T F F T T F F T F F F F F T T T Valid 7. P2 P1 ∴ M N N ⋅ ~N M ∨ (N ⋅ ~N) ~(N ∨ ~N) T T F T T T F F T T F T F F T F F F F T Valid 8. P1 P2 ∴ O P Q O ∨ P O ⋅ P (O ∨ P) ⊃ Q Q ⊃ (O ⋅ P) (O ∨ P) ⊃ (O ⋅ P) T T T T T T T T T T F F T F T T T F T T F T F F T F F T F F T F F T T T F T F F F T F T F F T F F F T F F T F T F F F F F T T T Valid Logic I Week 5 09/15 Pg 329 B 2. S p q p ⊃ q (p ⊃ q) ⊃ q p ⊃ [(p ⊃ q) ⊃ q] T T T T T T F F T T F T T T T F F T F T Tautology 3. S p q p ⋅ q p ⊃ ~ q (p ⋅ q) ⋅ (p ⊃ ~q) T T T F F T F F T F F T F T F F F F T F Contradiction 4. S p q q ∨ ~q ~p ⊃ (q ∨ ~q) p ⊃ [~p ⊃ (q ∨ ~q)] T T T T T T F T T T F T F F T F F T T T Tautology 6. S p q ~q p ⊃ p q ⋅ ~q (p ⊃ p) ⊃ (q ⋅ ~q) T T F T F F T F T T F F F T F T F F F F T T F F Contradiction Reviewing for Test Symbolizations pg 322 C *1. A ⊃ (B ⋅ C) ~B ∴ ~A Note: “then, if” is the main break. The test will not have any comma-happy problems like this. Logic I Week 5 09/15 2. D ⊃ (E ⊃ F) E ∴ D ⊃ F 9. C ⊃ (I ∨ R) (I ⋅ R) ⊃ B ∴ C ⊃ B Pg 323 5. M ⊃ (N ⊃ O) N ∴ O ⊃ M HOMEWORK # 9 DUE TUESDAY: PG 322 C 3, 4 (SYMBOLIZE BEFORE CREATING A TRUTH TABLE); PG 329 C 2, 3 Test on Thursday, 09/22 will include: 1. Symbolization section 2. Truth tables section a. Testing argument validity b. Practicing partition work i. Tautology ii. Contradiction iii. Contingent 3. MIGHT include a T/F section My study guide will be posted on StudySoup, and we will review some more in class on Tuesday. *Notes below are important, but are NOT on the test on Thursday. These are an introduction to what we will be learning in class AFTER the test. Logic I Week 5 09/15 Notes for after the test Essentially, we will be learning shortcuts to testing validity that bypass truth tables. 1. Rules of Inference (table on pg 343) a. Tautological conditionals (book calls them Elementary Valid Argument Forms) i. Ex. 1. [(p ⊃ q) ⋅ ~q] ⊃ ~p 2. p ⊃ (p ∨ q) b. Tautological biconditionals (book calls them Logically Equivalent Expressions) i. Ex. 1. ~(p ⋅ q) ≡ (~p ∨ ~q) c. Use Rules of Inference to simply look at an argument and analyze its validity. Write the steps used in lines below the original argument, and list to the right of each line which step you adapt and how (which elementary valid argument form or logically equivalent expression used to make the adjustment). i. Ex. 1. 1A ⊃ (B ⋅ C) ~B 2 /∴ ~A 3~B ∨ ~C 2 Add ~(B ⋅ C) DeM 4 3 5 ~A 1, 4T Argument is Valid ii. Examples of identifying the rule of inference from the text 1. *1. Absorption (A ⋅ B substituted for p, and C substituted for q) 2. *5. Constructive Dilemma 2. All premises T, with F conclusion a. In a given argument, to test its validity, we attempt to make all of the premises true, but the conclusion false. If this can be accomplished, the argument must be invalid. i. M ⊃ (N ⊃ O) N ∴ O ⊃ M ii. First we figure out what truth values we must have to make the conclusion false 1. O must be True and M must be False iii. Then, using those truth values throughout the argument, we must figure out what truth value(s) any other statement letters must have to create true premises. 1. N must be True to make P 2rue. M N O F T T Logic I Week 5 09/15 2. If M is False, N is True, and O is True, then P w1uld also be True. iv. Since we can create all true premises and a false conclusion using this argument, the argument must be invalid.

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