Logic I Exam I Study Guide
Logic I Exam I Study Guide PHL 1100
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This 26 page Study Guide was uploaded by Amanda Notetaker on Sunday September 18, 2016. The Study Guide belongs to PHL 1100 at Appalachian State University taught by Dr. Patrick Rardin in Fall 2016. Since its upload, it has received 36 views. For similar materials see Logic I in Philosophy at Appalachian State University.
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Date Created: 09/18/16
Logic I Study Guide Exam 1 – Thursday, 09/22/16 Created by Amanda Horsley Introduction Thanks for downloading! I hope this study guide is helpful! If you have any questions, want any tutoring, or want to give me feedback on my notes and study guide, please email me at email@example.com. Here are the links to all of the notes up until now: Week 1 – https://studysoup.com/note/2304338/asu-phl-1100-week-1-fall-2016 Week 2 Part 1 - https://studysoup.com/note/2304467/asu-phl-1100-week-2-fall-2016 Week 2 Part 2 - https://studysoup.com/note/2304495/asu-phl-1100-week-2-fall-2016 Week 3 Part 1 - https://studysoup.com/note/2308846/asu-phl-1100-week-3-fall-2016 Week 3 Part 2 – https://studysoup.com/note/2315064/asu-phl-1100-week-3-fall-2016 Week 4 Part 1 – https://studysoup.com/note/2315069/asu-phl-1100-week-4-fall-2016 Week 4 Part 2 – https://studysoup.com/note/2319902/asu-phl-1100-week-4-fall-2016 Week 5 Part 1 – https://studysoup.com/note/2322757/asu-phl-1100-week-5-fall-2016 Week 5 Part 2 - https://studysoup.com/note/2325547/asu-phl-1100-week-5-fall-2016 The test will consist of: • Symbolization section • Truth tables section • Testing argument validity • Practicing partition work • Tautology • Contradiction • Contingent • MIGHT include a T/F section • Vocabulary also included in this study guide Some Important Vocabulary Statement Argument • Statement Letters – Uppercase • Argument – a group of statement letters used to create a statement letters that contain at least one • Statement Variables – Lowercase premise and a conclusion letters used to create a statement • Argument form – a series of form statement variables that contains at • Statement form – a series of least one premise and a conclusion; statement variables that is the starting point for an argument; variables can be replaced with any starting point for a statement: simple or compound statement, as variables can be replaced with any long as it is consistent throughout simple or compound statement, as long as it is consistent throughout Examples Statement Argument • Letters= A, B, C • Argument form Variables = p, q, r p v q ~p • Statement form ∴ ~q ~p v q • Argument • Statement A v B ~A v B (simple) ~A -OR- ∴ ~B ~(A v B) v ~C (compound) Some Important Vocabulary (cont.) Converting Forms into Statements Validity or Arguments • Valid – if all of the premises are true,• Specific form – the form which has the conclusion MUST be true. been replaced with a 1:1 ratio of only • Invalid – an argument with all true simple statements(a single letter) premises and a false conclusion. for each variable in order to create a statement or argument • Sound – a valid argument whose • Ex.) p ⊃ (~p v q) premises are both true and correct. A ⊃ (~A v B) Truth-Functional Connectives • Used to symbolize English words in order to create forms, statements, and arguments. • Negation • Not, “it is not the case that” • Tilde (~) • Conjunction • And, but, yet, also, still, although, however, moreover,nevertheless • Dot (⋅) • Disjunction • Or, unless • Wedge (v) Truth-Functional Connectives (cont.) • Conditional • If, then, “only if” • Horseshoe (⊃) • “If” always goes with the antecedent, or the part before the horseshoe • “Then” and “only if” both always go with the consequent, or the part after the horseshoe • Biconditional • “If and only if” • Tribar (≡) Symbolization Turning English sentences into statements and arguments Statement Examples Al is happy or Al is not happy. A v ~A Neither Al nor Bill is happy. ~(A v B) It is not the case that Al is happy, and Bill is happy. ~A ⋅ B If Al is happy then Bettyis happy. A ⊃ B Al is happy if Betty is happy. B ⊃ A Cathy is happy only if Jane is not happy. C ⊃ ~J Al is happy if and only if Betty is happy. A ≡ B If Al is happy then Betty is happy, and Jane is not happy. (A ⊃ B) ⋅ ~J If Al is happy, then Betty is happy and Jane is not happy. A ⊃ (B ⋅ ~J) Argument Examples If Al is happy and Betty is not happy, then Jill is happy. Al and Betty are happy. So Jill is not happy. (A ⋅ ~B) ⊃ J A ⋅ B ∴ ~J Jill and Al will go to the movie only if Betty and Chris will go with them. Chris has too much homework to see a movie. So neither Jill nor Al will see a movie. (J ⋅ A) ⊃ (B ⋅ C) ~C ∴ ~(J v A) Chris will swim if both Betty and Jill swim. Not both Betty and Jill swim. Chris will swim. (B ⋅ J) ⊃ C ~(B ⋅ J) ∴ C Practice from the textbook Answers in the back of the book Statements • Pg 299 C 1, 5, 10, 15, 20, 25 • Pg 308 B 1 Also, look at Homework • Pg 309 B 6, 10, 15, 20 #2, #3, #4, and #5 • Pg 310 B 25 Arguments • Pg 322 C 1 (just symbolize) • Pg 323 5, 10 (just symbolize) Truth Tables Defining Validity Defining Truth-Functions Negation (~p) Conjunction (p ⋅ q) Disjunction (p v q) p ~p p q p ⋅ q p q p v q T F T T T T T T T F F T F T F T F T F F T T F F F F F F Defining Truth-Functions (cont.) Biconditional (p ≡ q) Conditional (p ⊃ q) p q p ⊃ q p q p ≡ q T T T T T T T F F T F F F T T F T F F F T F F T How to use those 5 tables: • value of statements. value of statement letters, you can determine the truth • For example: If G and H are true, and M and N are false, determine the truth value of the following statements: 1. ~G 2. H ⋅ M 3. N v G Answers on next slide 4. G ⊃ M 5. G ≡ H Answers and More 1. False For more practice, look in the text: 2. False Pg. 297 A 1 3. True Pg. 298 A 5, 10, 15, 20 4. False Pg. 299 A 25 B 1, 5, 10, 15, 20, 25 5. True Pg. 308 A 1, 5, 10, 15, 20, 25 Also, look at Homework #3, #4, and #5 Using Truth Tables to Determine Argument Validity • To do this, you MUST have the five tables (here and here) memorized. • 2 important formulas for creating truth tables for arguments: • 2 = the number of rows where n is the number of statement letters or variables • 1n= the number of Ts and Fs where n is the column number 2 • Those don’t make much sense out of context, I know. So let’s work through one. Practice (A ⋅ ~B) ⊃ J A ⋅ B ∴ ~J There are 3 letters, so 2 is 2 , or 8. That means there are 8 rows. In column #1, the fraction would be ½, which means ½ of the 8 rows are T, and the other ½ are F. In column #2, the fraction would be ¼, which means ¼ of the 8 rows T, ¼ F, ¼ T again, and ¼ F again. In column #3, the fraction would be 1/8, so the T and F would alternate every line. The table will look like the one on the next slide. A B J ~B A ⋅ ~B (A ⋅ ~B) ⊃ A ⋅ B ~J (A ⋅ ~B) ⊃ J T T T F F T T F A ⋅ B T T F F F T T T ∴ ~J T F T T T T F F T F F T T F F T Remember,an argument is only valid if the conclusion is true in all instances where the F T T F F T F F premises are all true. The yellow F T F F F T F T highlighting is where the premises are both F F T T F T F F true. As you can see, the conclusion is not F F F T F T F T true in every instance. The argument must be invalid. More Practice • Pg 313 Group A e, o Also, look at Homework #7, #8, and #9 • Pg 322 B 1, 5 C 1 • Pg 323 C 5, 10 Truth Tables Partition Work Important Information • The defining column (DC) is the last column in the truth table. Looking at the truth values in this column will tell you which partition that statement belongs in. • There are three partitions • Tautology • Only Ts in DC • Contradiction • Only Fs in DC • Contingent • At least one T and one F in DC • No statementmay be in more than one partition. • Every statement belongs in one of these partitions. Partitions TautologytradictiContingent DC DC DC p q p v ~p p ⋅ ~p q ⊃ (p ⋅ ~p) T T T F F T F T F T F T T F F F F T F T Practice • Pg. 329 B 1, 5, 10 Also, look at Homework C 1, 5, 10, 15, 20 #8 and #9
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