Truth-Functional Logic

Discussion: Truth-Functional Logic Required Resources Read/review the following resources for this activity: Textbook: Chapter 7 Lesson Minimum of 1 scholarly source Initial Post Instructions Consider some of the skills and knowledge you need to understand truth-functional logic. Forming the truth-functional claims means you have to have a good understanding of how English sentences are formed in order to convey accurate and precise meaning. Translating English sentences into symbolic language requires you to distinguish the parts of complex thought, put those thoughts into logical order, and make inferences from them. For the initial post, address the following: Determine how abstracting the parts of a truth-functional statement forces you to pay strict attention to the meaning and the validity of its logic. To get you started, reduce this statement to truth-functional symbolic form: “If I ask you to help me out, then I need your help; I need your help, so I must be asking for it.” Connect these skills to the things you will be doing in your professional life. Follow-Up Post Instructions Respond to at least two peers or one peer and the instructor. Further the dialogue by providing more information and clarification. Writing Requirements APA format for in-text citations and list of references Grading This activity will be graded using the Discussion Grading Rubric. Please review the following link: Link (webpage): Discussion Guidelines Course Outcomes (CO): 3, 4 Reply Reply to Week 4 Discussion: Truth-Functional Logic As we learn about truth-functions this week, the truth value of a compound proposition expressed in terms of one or more logical operators is said to be a function of the truth values of its components. This means that the truth value of the compound proposition is completely determined by the truth values of its components. If the truth values of the components are known, then the truth value of the compound proposition can be calculated from the definitions of the logical operators. For example, “Mary believes that Paul is dishonest” is compound because it contains the statement “Paul is dishonest” as a component. Yet, the truth value of the compound statement is not determined by the truth value of the component, because Mary’s beliefs about Paul are not compelled by any attribute that Paul may or may not possess. ~ (the ’tilde’ to symbolize ‘not’) • (the ‘dot’ to symbolize ‘and’) ν (the ‘wedge’ to symbolize ‘or’) ⊃ (the ‘horseshoe to symbolize ‘if…then…’) ≡ (the ‘triple bar’ to symbolize ‘if, and only if’) For any statements, p and q, ~ p “It is not the case that ‘p’ is the case.” p • q “Both ‘p’ is the case and ‘q’ is the case.” p • q “Either ‘p” is the case or ‘q’ is the case.” p • q “If ‘p’ is the case, then ‘q’ is the case.” p • q “‘p’ is the case, if, and only if, ‘q’ is the case.” are all COMPOUND STATEMENTS. Gentle Reminder: Use scholarly, outside resources in your posts to include citation(s) and reference(s). References McIntyre, M. (n.d.). Santa Barbara College. Propositional Logic. Chapter 6. Hurley, A concise introduction to logic. 6th. Ed., Wadsworth Publlshing, Belmont: CA.

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