Symbolic Logic (PHIL 4160)
Spring 2012

Study Guide for Test 4—Final Exam [REVISED April 17]

·         Date: Thursday April 26, 8-10:30am

·         You will need to supply your own paper (either notebook paper or a blue book is fine).

·         This test will be worth 30% of your total course grade. Possible score: 100 out of 100 points.

·         This is a timed test. You will have two and a half hours to complete it.

A. TRANSLATION INTO SYMBOLIC LOGIC (18%)

Translation into Sentential Logic

·         2 problems worth 2 points each; 4 points total.

·         similar problems are in your textbook: exercises 2-3, 2-4, 2-5, 2-6, and 2-7

·         INSTRUCTIONS: "Symbolize the following sentences, using sentence constants to represent atomic sentences."

Translation into Predicate Logic

·         7 problems worth 2 points each; 14 points total.

·         similar problems are in your textbook: exercises 7-1, 7-3, 7-4, 7-5, 7-6, 7-9, 7-10, 10-1, 10-2 (ignore the requirement to construct expansions), 10-3, 10-4, 10-5, 10-6, 13-2, 13-3

·         INSTRUCTIONS: “Symbolize the following sentences, using the indicated letters. Indicate as much logical structure as possible in your symbolization. Assume an unrestricted domain of discourse. Some translations will require the use of the identity symbol.”

B. TRANSLATION INTO ENGLISH (12%)

Translation from Sentential Logic

·         2 problems worth 2 points each; 4 points total.

·         similar problems are in your textbook: exercise 2-8

·         INSTRUCTIONS: “Translate the following into more or less colloquial English sentences, using the following sentence constants...”

Translation from Predicate Logic

·         4 problems worth 2 points each; 8 points total.

·         similar problems are in your textbook: exercises 7-7, 10-7

·         INSTRUCTIONS: “Translate the following into English, being as colloquial as possible. Assume an unrestricted domain of discourse and use the following property constants and individual constants...”

C. PROOFS (70%)

Sentential Logic Proofs

·         3 problems worth 7 points each; 21 points total.

·         similar problems are in your textbook: exercises 4-2, 4-5, 4-6, 4-8, 4-9, 4-10, 4-11, 4-12, 5-1, 5-2 [which refers back to 4-13], 5-3, 5-4, 5-5

·         INSTRUCTIONS: “Use the proof method to demonstrate that each of the following arguments are valid. You may use the original 18 rules, plus CP and IP.”

Predicate Logic Proofs

·         7 problems worth 7 points each; 49 points total.

·         similar problems are in your textbook: 9-1, 9-3, 9-5, 10-10, 10-11*, 10-13*, 10-14*, 13-1

·         INSTRUCTIONS: “Use the proof method to demonstrate that the following arguments are valid. You may use any rules we have covered (the original 18 rules, CP, IP, the five quantifier rules, and the two identity rules).”

*These exercises have not been assigned as homework. You may nevertheless wish to work some or all of them as practice before your final exam.

D. PROPERTIES OF RELATIONS (6%)

·         4 problems worth 1.5 points each; 6 points total

·         INSTRUCTIONS: “Determine the status of the following relations with respect to symmetry, transitivity, and reflexivity."

·         similar problems are in your textbook: exercise 13-4 (part A)