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October 29, 2003 13:49
k35-appb
Sheet number 1 Page number 4
cyan black
APPENDIX
B
SOLUTIONS AND HINTS TO SELECTED EXERCISES
Section 1.1
1. Common form: If p then q. p. Therefore, q. (a + 2b)(a 2 ? b) can be written in pre?x notation. All algebraic expressions can be written in pre?x notation. 3. Common form: p ¡ý q. ¡p. Therefore, q. My mind is shot. Logic is confusing. 5. a. It is a statement because it is a true sentence. 1,024 is a perfect square because 1,024 = 322 , and the next smaller perfect square is 312 = 961, which has less than four digits. 6. a. s ¡ü i b. ¡s ¡ü ¡i 8. a. (h ¡ü w) ¡ü ¡s d. (¡w ¡ü ¡s) ¡ü h 10. a. p ¡ü q ¡ü r c. p ¡ü (¡q ¡ý ¡r) 11. Inclusive or. For instance, a team could win the playoff by winning games 1, 3, and 4 and losing game 2. Such a team would satisfy both conditions. 12. ¡°United States President¡± AND (14th OR fourteenth) AND NOT amendment. 14. p q ¡p ¡p ¡ü q T T F F T F T F F F T T F F T F
16.
p T T T T F F F
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