Test 6 Logic Name Chapter 6 Test

Test 6test 6logicname Chapter 6 Testex

Test 6test 6logicname Chapter 6 Testex

Test 6 Test 6 Logic Name:______________________________ Chapter 6 Test Except for the truth table questions (which are double credit), each question is worth 2 points. Write your answer on the form provided. Erasure marks may cause the grading machine to mark your answer wrong. Select the correct translation for the following problems.

Paper For Above instruction

The provided questions involve translating natural language propositional logic statements into symbolic form, evaluating their truth values under given conditions, and analyzing their logical relationships using truth tables and formal argument forms.

Introduction

Logic is a critical field in philosophy, computer science, linguistics, and mathematics, offering tools for formal reasoning. The ability to translate complex statements into symbolic logic, evaluate their truth values systematically, and analyze their logical relationships allows for rigorous argument assessment, verification of validity, and understanding of logical entailments. This paper approaches the assignment by tackling translation tasks, truth value evaluations using truth tables, and identifying arguments' validity through formal reasoning.

Part 1: Translating Natural Language into Symbolic Logic

The initial set of questions (1-10) requires translating statements about various firms and their actions into propositional logic. This process involves identifying propositional variables (e.g., P for Princess, O for Oceania, etc.) and using logical connectives such as conjunction (•), disjunction (˅), negation (¬), and implication (→). Accurate translation is essential for subsequent truth table evaluations and logical analysis.

For example, question 1 states: "Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares." The correct translation involves recognizing the disjunction between Princess dropping its dress codes (P) and Oceania enlarging its fleet (O), combined conjunctively with Seabourn reducing fares (S):

a. P • (O ˅ S)

b. (P • O) → S

c. P → (O • S)

d. P → O • S

e. (P → O) • S

The correct answer is (b), which captures the implication if Princess drops its dress codes and Oceania enlarges its fleet, then Seabourn reduces its fares.

Part 2: Truth Value Evaluation using Truth Tables

The assignment includes constructing truth tables for logical statements like "(R • B) → (B → R)", analyzing their tautologicality (always true), contingency, or contradiction. Counting the number of lines in the truth tables (e.g., 4, 8, 16) helps determine the complexity of the statement. For example, "(R • B) → (B → R)" is a tautology with 8 lines in its truth table, as it is true under all truth value combinations.

Part 3: Analyzing Logical Equivalence and Argument Validity

Some questions involve analyzing whether pairs of statements are logically equivalent, contradictory, or consistent. For instance, the statements "G ‡¬H" and "H ‡¬G" are contradictory because they cannot both be true simultaneously but can both be false, indicating inconsistency.

Arguments are evaluated for validity using argument forms like modus ponens (MP), modus tollens (MT), disjunctive syllogism (DS), and hypothetical syllogism (HS). Correct identification of the argument form confirms validity if the conclusion necessarily follows from the premises.

Part 4: Using Indirect Truth Tables

Some problems require constructing indirect truth tables to test validity, which involves assuming the negation of the conclusion and checking for contradictions with the premises. If a contradiction arises under all valuations, the argument is valid.

Part 5: Identification of Argument Forms

Finally, certain problems ask to identify the named logical form of given arguments, such as affirming the consequent (AC), modus ponens (MP), disjunctive syllogism (DS), hypothetically valid (HS), or invalidity if no recognized form applies. This classification aids in understanding the nature of the reasoning involved.

Conclusion

This comprehensive approach, involving translation, truth table construction, validity testing, and form identification, exemplifies key skills in propositional logic. Mastery of these techniques enables rigorous examination of logical statements and arguments, fostering clearer reasoning and better philosophical and computational analysis.

References

  • Hacker, P. M. (2014). Logic: The Basics. Routledge.
  • Copi, I. M., Cohen, C., & McMahon, K. (2014). Introduction to Logic. Pearson.
  • Hurley, P. J. (2014). A Concise Introduction to Logic. Cengage Learning.
  • Ladusaw, W. A. (2016). Introduction to Logic. McGraw-Hill Education.
  • Johnson-Laird, P. N. (2010). Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness. Harvard University Press.
  • Irving M. Copi. (2011). Symbolic Logic. Routledge.
  • Barwise, J., & Etchemendy, J. (2019). Language, Proof, and Logic. CSLI Publications.
  • McCarthy, J., & Hayes, P. (2019). Some Philosophical Problems from the Standpoint of Artificial Intelligence. CRC Press.
  • Benjamin, A. (2018). Logic and Philosophy: A First Course. Routledge.
  • Thomason, R. H. (2009). Logic for Philosophers. University of Chicago Press.

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