Logic Problems and Solutions: Proofs of Logical Statements, Assignments of Discrete Structures and Graph Theory

Download Logic Problems and Solutions: Proofs of Logical Statements and more Assignments Discrete Structures and Graph Theory in PDF only on Docsity! Hw2 Due (1/22/09) Note: You may refer to the answers to some of the problems given at the back of the textbook. 1. Pg 382 3(a). Find the number of premises required for a proof of the following wff. Assume that the letters stand for other wffs. 3a. A → (B → (C → D)). 2. Pg 382. 5(b, c) Give formal proofs of each of the following tautologies by using the CP rule. 5b. A → (B → (A  B)). 5c.(A  B → C)  A → C. 3. Pg 382. 6(a, b) Give formal proofs for each of the tautologies using the IP rule. 6a. A → (B → A). 6b. (A → B)  (A  B) → B. 4. Pg 383. Question 8. Give a formal proof of the equivalence. A  B  C  A  (B  C). In other words, prove both of the following statements. Use either CP or IP. 8a. (A  B  C)  (A  (B  C)). 8b. (A  (B  C))  (A  B  C). 5. Pg 393. Question 3(a, c). In the Hilbert- Ackermann axiom system, prove each of the following statements. Do not use the CP rule. 3a. (A  B)  ((C  A)  (C  B)). 3c. A  A.