1. Study Questions for Quiz 6 The exam has three parts: 1. (40 pts) Translation in Predicate Logic 2. (50 pts) Using Proofs and Trees to test Concepts from Ch. 12, 13 3. (30 pts) Explaining the tests

2. Study Questions for Quiz 6 1. (40 pts) Translation in Predicate Logic There will be about 10 sentences to translate. Sample: Translate using the notation provided. Add missing dictionary items in the blanks to the right. a. Al Gore lost the electionLx = x lost the election _______ Al Gore Solution: La a = Al Gore b. A whale is a mammal Mx = x is a mammal ______ whale Solution: $x(Wx>Mx) Wx = x is a whale You need to know these: all, some, no, each, every, only, none but, any, a, not all See p. 11 of Predicate Logic for information on dictionaries.

3. Study Questions for Quiz 6 2. (50 pts) Using Proofs and Trees to Check Concepts Sample: With both proofs and trees show the following of statements are equivalent: (S&T)>R, T>(-R>-S) You may omit dependency lists in your proofs. Solutions: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. (S&T)>R T -R S S&T R R&-R -S -R>-S T>(-R>-S) A PA 4,2 &I 1,5 >O 6,3 &I 4-7 –I 3-8 >I 2-9 >I 1. 2. 3. 4. 5. 6. 7. 8. T>(-R>-S) S&T S T -R>-S S>R R (S&T)>R A PA 2, &O 1,4 >O 5 CN 6,3 >O 2-7 –I (S&T)>R -(T>(-R>-S)) T -(-R>-S) -R --S -(S&T) R * -S -T * * T>(-R>-S) -[(S&T)>R] S&T -R S T -T -R>-S *. --R -S *

4. Study Questions for Quiz 6 3. (30 pts) Explaining the Tests There will be about 6 questions of the form: How do you show that ____ is ___ with a ___? Sample: Briefly answer each question. a.How do you show that A is a logical truth with a tree? Solution: the tree for –A closes. b.How do you show that A and B are consistent with a truth table? Solution: The table has a row where A and B are T together.