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*?*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 wonÕt have to do a truth tree but
youÕll 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