Spring 2016: Final Exam Review

I Write the letter of the correct answer in the space provided at the beginning of each sentence. (10 – 20) multiple choice questions @ 1 point each: 10 - 20 points total)

To answer these questions you should understand the following concepts:

• Validity: What is it for an argument to be valid? What, if anything, do features of an argument show about its validity? E.g. what, if anything, do consistent premises or inconsistent premises, a tautologous conclusion or a self-contradictory conclusion, show? Etc.
• Soundness and Completeness: What is meant by saying that the rules of propositional logic are truth-preserving and why is this of significance? What is semantic consequence? What is derivability? What is meant by saying that the system of propositional logic is sound? What is meant by saying that the system of propositional logic is complete.
• Conditional and indirect proof: How can you show that a set of sentences is inconsistent using natural deduction (i.e. proof, as in Chapter 7)? How does indirect proof show validity? What assumptions are strategically correct when doing conditional and indirect proof?
• Predicate Logic: What do the individual constants and predicates of predicate logic designate? How do we understand singular sentences ascribing properties to individuals in terms of set membership? How do we understand singular sentences ascribing relations to individuals in terms of set membership? What do universally quantified and existentially quantified general sentences say about the emptiness or non-emptiness of sets? How are emptiness and non-emptiness represented on Venn diagrams?

II Which of the following symbolized sentences in predicate logic, if any, is (are) correct translations of the following English sentences? (5 multiple choice questions @ 1 point each: 5 total)

III Truth tree. What does the following truth tree tell you? You won’t have to do a truth tree but you’ll be given a completed truth tree that tests for validity and asked questions like: what the conclusion of the argument it tests is, whether the argument is shown to be valid or invalid, if invalid what assignment(s) of truth values to sentence letters makes the premises true and conclusion false, and what the tree shows about the consistency or inconsistency of initial sentences. (5 true/false questions @ 1 point each: 5 total)

IV Derive the conclusions of the following symbolized arguments. You may use all 19 rules, conditional and indirect proof where appropriate (2 problems @ 5 points each: 10 total)

V Use conditional proof or indirect proof and the 19 rules of inference where appropriate to establish the truth of the following tautology (1 problem @ 5 points: 5 total)

Last Things

Exams: 9:15 Section: Thu May 12: 8:00 am - 10:00 am in Camino 112

10:45 Section: Tue May 17: 11:00 am - 1:00 pm in Camino 112

Exam Week Office Hours: Wed May 11: 9:30 am – 2:30 pm; Mon May 16: 9:30 am – 2:30 pm.

Remember, to make appointments or chat you can reach me at: email (preferred): baber@sandiego.edu;
or cell phone: (619) 805-6838 (voice or text)