ITEC 122 2008fall ibarland

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hw03
First Order Logic

Depending exactly where we get on Sep.17 (Wed)'s lecture, problems will be tailored to those topics.

1. (3pts) Rosen 6ed: p61, #33 (= Rosen 5ed: p55, #33): Pushing negation over quantifiers, (a)-(e).
2. (5 pts.) TeachLogic exercises III: #11 (ducks and officers; based on Rosen, §1.3, pg.44, #58.

   Hint:Express all formulas using ∀, to make your life easier for part (d).

   1. No ducks are willing to waltz.
   2. No officers ever decline to waltz.
   3. All my poultry are ducks.
   4. My poultry are not officers.
   5. Does (d) follow from (a), (b), (c) ? Argue informally; you don't need to use the algebra or inference rules for first-order logic here.
3. (4pts) TeachLogic exercises III: #12 (an even prime?)
4. Extra Credit (4pts): TeachLogic exercises III: #13 (interpretations). For "WaterWorld", you may think "Minesweeper".
5. Extra Credit (4pts): TeachLogic exercises III: #15 (translating sayings into first-order logic)
6. Extra Credit (4pts): TeachLogic exercises III: #18 Writing formulas about sequences.
7. (5pts) Rosen 6ed: p72, #4 (= Rosen 5ed: p73, #2): Which rule of inference used in the English arguments about... Kangaroos in Australia, etc.
8. (5pts) Rosen 6ed: p72, #6 (= Rosen 5ed: p73, #4): Create an argument about sailing weather.
   Like a geometry proof, each line of your answer is a statement, plus (on the right) a justification which is either "premise" or one of the rules from Rosen's Table 1.¹
9. (8pts) Rosen 6ed: p73, #10 (= Rosen 5ed: p73, #8): Find a relevant conclusion, with a justification; sore hockey etc..

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