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# Logic I Notes, Week 5, Class 09/13 PHL 1100

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This 6 page Class Notes was uploaded by Amanda Notetaker on Thursday September 15, 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 4 views. For similar materials see Logic I in Philosophy at Appalachian State University.

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Date Created: 09/15/16

Logic I Week 5 09/13 Homework #7 Answers 12. P 1 P2 ؞ p q r pכ q q כr rכ p T T T T Invali T T T T F T d F T T F T F T T T F F F T T F T T T T F F T F T F T F F T T T F F F F T T T 13. P1 P2 ؞ p q r pכ (qכ r) p כq p כr T T T T T T T T F F T F T F T T F T T F F T Valid F F F T T T T T F T F T T T F F T T T T F F F T T T 14. P P ؞ 1 2 p q r pכ (q ∙ r) (q ᵛ כ)~p ~p T T T T F F T T F F F F T F T F Valid F F T F F F T F F T T T T T F T F T T T F F T T T T F F F T T T Truth Tables 1. Define truth functions (foכ, and ≡), 2. Calculate truthvalues Logic I Week 5 09/13 3. Determine validity 4. Partition our truthfunctional statements a. Tautology (only “T”s in defining column) into one of these. b. Contradiction (only “F”s in defining column) c. ConNo statement can be T and 1 F in defining column) in more than one. The defining column (D.C.) for a statement of interest is the last one in the truthtable. Examples D.C. p q p ᵛ ~p T T T Tautolog T Fy T F T T F F T D.C. p q p ᵛ ~p p ∙ ~p T T T F T F T Contradicti F F T T F on F F T F D.C. p q p ᵛ ~p p ∙ ~p qכ (p ∙ ~p) T T T F F Contingent T F T F T F T T F F F F T F T Biconditional ≡ is a tribar ≡ means “if and only if” in English A biconditional can only be true if all of the variables or letters have the same truth value. p q p ≡ q T T T T F F F T F F F T Logic I Week 5 09/13 Practice questions from textbook Pg 329 B *1. D.C. p q p כq pכ (pכ q) [pכ (pכ q)]כq T T T T T T F F F ContiTge nt F T T T T F F T T F *5. D.C. p q q ∙ ~q pכ (q ∙ ~q) pכ [pכ(q ∙ ~q)] T T F F F T F F F Continge F T F T T F F F T nt T *C5. D.C. p q p ᵛ q p ∙ (p ᵛ q) p ≡ [p ∙ (p ᵛ q)] T T T T T T F T T TautolTgy F T T F T F F F F T HOMEWORK # 8 DUE 09/15: PG 322 B 3, 4, 7, 8; PG 329 B 2, 3, 4, 6; READ 9.1 AND 9.2 NOTE: EXAM 1 RESCHEDULED TO THU. 09/22 I WILL POST A STUDY GUIDE NO LATER THAN SUNDAY, 09/18. Logic I Week 5 09/13 Homework #7 Answers 12. P 1 P2 ؞ p q r p כq q כ r rכp T T T T T T Invalid T T F T F T T F T F T T T F F F T T F T T T T F F T F T F T F F T T T F F F F T T T 13. P1 P 2 ؞ p q r p כ(qכ r) pכq p כ r T T T T T T T T F F T F T F T T F T Valid T F F T F F F T T T T T F T F T T T F F T T T T F F F T T T 14. P1 P2 ؞ p q r p כ(q · r) (q כ~p ~p T T T T F F T T F F F F T F T F F F T F F F T F Valid F T T T T T F T F T T T F F T T T T F F F T T T Truth Tables 1. Define truth functions (fכr, and ≡), 2. Calculate truth-values 3. Determine validity Logic I Week 5 09/13 4. Partition our truth-functional statements Every statement falls into a. Tautology (only “T”s in defining column) one of these. b. Contradiction (only “F”s in defining column) No statement can be in c. Contingent (at least 1 T and 1 F in defininmore than one. The defining column (D.C.) for a statement of interest is the last one in the truth-table. Examples D.C. p q p ᵛ ~p T T T T F T Tautology F T T F F T D.C. p q p ᵛ ~p p · ~p T T T F T F T F F T T F Contradiction F F T F D.C. p q p ᵛ ~p p · ~p כ (p · ~p) T T T F F T F T F T Contingent F T T F F F F T F T Biconditional ≡ is a tri-bar ≡ means “if and only if” in English A biconditional can only be true if all of the variables or letters have the sametruth value. p q p ≡ q T T T T F F F T F F F T Logic I Week 5 09/13 Practice questions from textbook Pg 329 B *1. D.C. p q pכ q p כ(pכ q) [pכ(p כq)]כq T T T T T T F F F T Contingent F T T T T F F T T F *5. D.C. p q q · ~q pכ(q · ~q) כ [pכ(q · ~q)] T T F F F T F F F F F T F T T Contingent F F F T T *C-5. D.C. p q p ᵛ q p · (p ᵛ q) p ≡ [p · (p ᵛ q)] T T T T T T F T T T Tautology F T T F T F F F F T HOMEWORK # 8 DUE 09/15: PG 322 B 3, 4, 7, 8; PG 329 B 2, 3, 4, 6; READ 9.1 AND 9.2 NOTE: EXAM 1 RESCHEDULED TO THU. 09/22 I WILL POST A STUDY GUIDE NO LATER THAN SUNDAY, 09/18.

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