I have saved some examples of exercises in formal logic which I spotted floating across the Internet. Students new to proofs and mathematical thinking might appreciate the extra exercise. Those in the know will recognize that the first few test propositional or sentential logic; the ones at the end add the use of quantifiers. ============================================================================== From: dbush@csugrad.cs.vt.edu (David Bush) Newsgroups: sci.math,sci.logic,rec.puzzles Subject: WFF'N'PROOF: Tardy Bus Puzzle Date: 16 Aug 1995 12:25:07 -0400 For those who might be interested in the game of WFF'N'PROOF, here is a logic puzzle from the beginning of the instruction manual. Of course, the words "if," "then," "and," "or," "not," and "only" have a very precise meaning here. The Tardy Bus Problem. Given the following statements as premises: 1) If Bill takes the bus, then Bill misses his appointment, if the bus is late. 2) Bill shouldn't go home, if (a) Bill misses his appointment, and (b) Bill feels downcast. 3) If Bill doesn't get the job, then (a) Bill feels downcast, and (b) Bill should go home. Is it valid to conclude: Q1 that if Bill takes the bus, then Bill does get the job, if the bus is late? Q2 that Bill does get the job, if (a) Bill misses his appointment, and (b) Bill should go home? Q3 that if the bus is late, then (a) Bill doesn't take the bus, or Bill doesn't miss his appointment, if (b) Bill doesn't get the job? Q4 that Bill doesn't take the bus, if (a) the bus is late, and (b) Bill doesn't get the job? Q5 that if Bill doesn't miss his appointment, then (a) Bill shouldn't go home, and (b) Bill doesn't get the job? Q6 that Bill feels downcast, if (a) the bus is late, or (b) Bill misses his appointment? Q7 that if Bill does get the job, then (a) Bill doesn't feel downcast, or (b) Bill shouldn't go home? Q8 that if (a) Bill should go home, and Bill takes the bus, then (b) Bill doesn't feel downcast, if the bus is late? Here's the company's address: WFF'N'PROOF PUBLISHERS 1490 South Boulevard Ann Arbor, Michigan 48104-4699 (313) 665-2269 [...] EQUATIONS is a similar game, sold by the same people, but uses arithmetic expressions instead of symbolic logic. It's perhaps more approachable. I prefer Equations, maybe because I've actually PLAYED it, even though the manual is the pits... ============================================================================== Subject: Only a logician... If you can lead it to water and force it to drink, it isn't a horse. ============================================================================== From: yu152979@yorku.ca Newsgroups: sci.math.symbolic Subject: Try to solve this Syllogism/Logic Problem Date: Tue, 05 Nov 1996 23:04:55 GMT The Pork-Chop Problem Problem: To achieve the complete Conclusion. 1. A logician, who eats pork-chops for supper, will probably lose money; 2. A young man always gets up at 5 a.m., unless he has lost money; 3. No earnest man, who does not eat pork-chops for supper, need take to cab-driving, unless he gambles; 4. A logician, who is in danger of losing money, had better take to cab-driving; 5. A gambler, whose appetite is not ravenous, will probably lose money; 6. A man who is depressed, having lost money and being likely to lose more, always rises at 5 a.m. 7. A man, who neither gambles nor eats pork-chops for supper, is sure to have a ravenous appetite; 8. A lively man, who goes to bed before 4 a.m., had better take to cab driving; 9. A man with a ravenous appetite, who has not lost money and does not rise at 5 a.m., always eats pork-chops for supper; 10. An earnest gambler, who is depressed though he has not been losing money, is in no danger of losing any; 11. A man, who does not gamble, and whose appetite is not ravenous, is always lively; 12. A lively logician, who is really in earnest, is in no danger of losing money; 13. A man with a ravenous appetite has no need to take cab-driving, so long as he is really in earnest; 14. A gambler, who is depressed though in no danger of losing money, sits up till 4 a.m. 15. A man, who has lost money and does not eat pork-chops for supper, had better take to cab-driving, unless he gets up at 5 a.m. 16. A gambler, who goes to bed before 4 a.m., need not take to cab-driving, unless he has a ravenous appetite; 17. An old man, who does not gamble, and who has not lost money though he is in danger of doing so, always eats pork-chops for supper; 18. A man with a ravenous appetite, who is depressed though in no danger of losing money, is sure to be a gambler. ============================================================================== From: brutii@aol.com (Brutii) Newsgroups: sci.math Subject: Predicate Calculus Date: 18 Dec 1996 15:01:32 GMT Given 1. Gretsky is a Ranger. 2. Messiea is a Ranger. 3. Kovaleu is a Russian. 5. All Rangers are hockey players. 6. All hockey players are Canadians or wish they were Canadians. 7. All Canadian hockey players want to win the stanley cup. 8. The Rangers won the Stanley cup in 1994. 9. Islander fans hate the Rangers. 10. Islander fans cheer for whoever plays the Rangers. 11. If team you cheer for loses, you are unhappy. 12. Messiea is the captain of the Rangers. 13. All Rangers respect the captain. 14. Keina is a traitor. 15. All Rangers hate keina or would like to play for him in St.Louis. (A) Translate this into predicate Calculus. (B) Draw a conclusion. (C) Prove that the Islander fans were unhappy in 1994. ============================================================================== From: CooLa Newsgroups: sci.math Subject: First-Order Logic Date: Sat, 26 Oct 1996 17:26:02 -0400 [...] Express the sentience in term of First-Order Logic: There is no barber who will shave percisely those men who do not shave themselves. quantifier : for all men Bx : x is a barber S(a,b) : a shaves b. [...] ============================================================================== @>Can anyone negate this sentence: @>"In every village, there is a person who knows everybody else in that @>village." Here's a WRONG answer: @There is at least one village in which at least one person @is not known by anyone else in the village. (although it's close!) What is an answer to the original question, and why is the above response incorrect? ==============================================================================