Group Exercises Week 4 (Sept. 23, 2011)Group 1

Section: ______

Write the names of the people in your group here (necessary condition for getting credit for today's attendance/participation):

Task 1: Decide which of the below exercises you would like to present to the class and who your group presenter(s) will be, if called upon.

Task 2: Work through as many of the following exercises as you can in the time available, starting with the exercise you plan to present to the class if called upon. Please record your answers on this sheet as you go along (feel free to use a piece of scrap paper if needed). Please label any extra sheet(s) with your group number and section number (e.g., Group X, Section 0X). Each group should turn in one set of work of all of your work to me before leaving class so that I can get a sense of how people are doing with the material (this work will not be graded but you will receive feedback, so the more work you show, the more feedback you get! ).

Don't worry if you don't complete all the exercises or even if you have difficulties completing any of them in full. Just do the best you can, working together as a group, and feel free to ask me for help at any time.

Exercise 1: Truth-Functionally Compound or Not?

For each of the following:

a)Determine whether it is truth-functionally compound statement or not. (Recall that if a statement is not truth-functionally compound, then it is truth-functionally simple and thus we will treat it as a simple sentence for the purposes of sentential logic)

b)State all of the truth-functionally simple components as complete propositions and give the abbreviation for that simple component (e.g., C = I like cats)

c)Symbolize the sentence using the abbreviations given in Part b.

  1. I will either get a puppy or a guppy, or possibly both.
  2. You may get either a puppy or a guppy, but not both.
  3. You may get neither a puppy nor a guppy.
  4. Lina is sad that she cannot get a guppy.
  5. Rosie is happy that we cannot get a puppy, but she is sad that we cannot get a guppy.
  6. Lina thinks that a betta would make a better pet than a guppy anyway.
  7. Lina wants a betta because they are easy to take care of.
  8. It is necessary that we get a hardy fish, because it is sad when they die.
  9. Neither Tom nor Lina nor Karin are in the market for a new cat.
  10. Lina wants to get a new hamster if Rowan won't stay out of the teapot, unless she thinks that a gerbil would be better behaved.

Presentation instructions for Exercise 1: If you choose to do your presentation on Exercise 1 then you need to present at least three examples, and you need to present all the steps for each example.

Exercise 2:Symbolizing Statements

For each statement below, symbolize the statement using the following conventions:

-Letters for abbreviating simple statements will be indicated by printing certain words in all caps. E.g., "I am a CROOK" would be abbreviated by the letter C. Where this will be problematic a dictionary will be provided.

-Letters will abbreviate affirmative statements. Thus, for the statement "I am not a CROOK," this will be symbolized as ~C, where C = I am a crook.

For each statement, complete the following steps:

a)Rewrite the statement in "Loglish" (half English/half logic) as follows: Leaving the logical words ("if," "and," "or," "not" and "if and only if") and punctuation in place, remove the simple statements and replace them with their abbreviations.

b)Symbolize the statement.

Part A: Straightforward ("easy") symbolizations

  1. If you were a PENGUIN, you'd UNDERSTAND how it is to be a penguin.
  2. It's not always GRAND [to be a penguin].
  3. If you were a PENGUIN, you'd LOOK around, and SEE nothing but penguins and FROZEN ground.
  4. You have nowhere to HIDE if you are a PENGUIN.
  5. I want to be COOL like the polar bear guys.
  6. I want to be TALL and somewhat MYSTERIOUS.
  7. Nothing profound comes in penguin SIZE.
  8. I'm a little too CUTE.
  9. I'm all DRESSED up but I've got no PLACE to go.
  10. We can't even FLY!

Part B: Tricky operators ("only if," "unless," "neither/nor," etc.)

  1. You will TRANSLATE this statement correctly only if you REMEMBER how to translate statements with "only if."
  2. You will TRANSLATE this statement correctly unless you FORGET how to translate statements with "unless."
  3. Writing your NAME on this paper is a necessary condition for getting CREDIT for today's attendance/participation.
  4. Writing your NAME on this paper and participating ACTIVELY in the class discussion are sufficient conditions for getting CREDIT for today's attendance/participation.
  5. You will not get both an A and a B in this class. (A = You will get an A in this class, B = You will get a B in this class)
  6. You will get neither an A nor a B in this class unless you STUDY hard. (A = You will get an A in this class, B = You will get a B in this class)
  7. PHILLIP and I will both not be having office hours today. (I = I will have office hours today)
  8. If you TAKE the logic exam without STUDYING, you will probably not do WELL.
  9. If a formula A is a NECESSARY condition for another formula B, then B is a SUFFICIENT condition for A.
  10. KISS me and I'll turn into a handsome PRINCE.

Part C: Complex formulas

  1. I GAIN weight if and only if I don't DIET, provided I am not MOTIVATED and neither SWIM nor RUN.
  2. Unless I am depressed or LAZY, I DIET or EXERCISE if I GAIN weight, provided I am MOTIVATED and don't get too TIRED. (P = I am depressed)
  3. I'll buy a BIKE and get FIT provided the city builds a bike PATH and I don't KEEP my gas guzzler or buy a NEW or USED car.
  4. If I don't buy a BIKE and I either KEEP my gas guzzler or buy a NEW or USED car, then I won't get FIT and will either contribute to global WARMING or CONSUME a lot of natural resources.
  5. It is not the case that I'll get FIT only if I get a BIKE, but unless I get a bike I won't QUIT smoking and I'll GAIN weight.
  6. I won't both contribute to global WARMING and CONSUME a lot of natural resources if I don't get a NEW or USED car, provided the city builds a bike PATH and I get a BIKE.
  7. Stock prices will FALL and the ECONOMY will fail to improve if interest rates RISE and the DEFICIT is not reduced, unless either more JOBS are created or there is a boom in HOUSING.
  8. Neither stock prices nor consumer SPENDING will fall, provided UNEMPLOYMENT does not rise and there is a boom in either the HOUSING or the AUTOMOBILE industry. (F = Stock prices will fall)
  9. Stock prices will FALL and either interest rates or UNEMPLOYMENT will rise, unless either the DEFICIT is reduced and the ECONOMY improves or TAXES are not raised and consumer spending increases. (R = Interest rates will rise, S = Consumer spending falls)
  10. More JOBS will be created and the ECONOMY will improve only if GOVERNMENT spending is increased and TAXES are not raised; however, the DEFICIT will be reduced only if taxes are raised and government spending is not increased, and the economy will improve if and only if the deficit is reduced.

Presentation instructions for Exercise 2: If you choose to do your presentation on Exercise 2 then you need to present one from each section (Parts A, B and C), presenting both steps for each example.

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