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Numbers and Their Application to Math and Science

Odd Solutions for HW Numbers Lesson 5

    Given p = "This is a frog.", q = "It should croak." Write out in words the following:
  1. Conditional (p=>q).
    A. If this is a frog, then it should croak.

  3. Converse (q=>p).
    A. If it should croak, then this is a frog.

  5. Biconditional (p<=>q).
    A. This is a frog if and only if it should croaks.
  7. Given the compound statement: My sister, who cooks whenever she can, loves cooking for people as long as they are appreciative of her labors. Write this statement in shorthand, symbolically identifing each piece.
    A. p = people are appreciative of her labors    
    q = she loves cooking for them      p=>q.

  9. Lots of advertising tries to appeal to a human need to belong. Write a counterexample for the following suggestive advertisements. "You'll be cool if you buy Converse shoes." "Buy a Lexus automobile, then everyone will be dripping with envy."
    A. Clothing doesn't make a person "cool".
    Not everyone is impressed with a Lexus.


  11. Write the converse and state if it is true: If you are a driver, then you are at least 16.
    A. If you are at least sixteen, then you are a driver. False. Some people don't learn how to drive until they are over eighteen.

  13. "If you go fishing, you are sure to hook a mackerel." You bring home a mackerel for supper. Did you catch it? Explain your answer.

    A. One isn't able to determine if you caught the fish. You could have bought it at a store and not gone fishing. (In cases like these, if the antecedent is true only then is the consequence true.)

  15. What is the conclusion of: "If a nail is lost, then a shoe is lost. If a shoe is lost, then a horse is lost. If a horse is lost, then a rider is lost. If a rider is lost, then a battle is lost. If a battle is lost, then a kingdom is lost."?
    A.If a nail is lost, then a kingdom is lost.

  17. Base 26 can be fun. Convert your first name from base 26 into base 10. Try to restrict your first name to 6 letters to avoid 32-bit integer overflow. Let A=1, B=2, ..., Y=25, Z=0, ignore upper/lower case.
    Answer: varies—see separate sheet

  19. Read 2.2, 2.3 of your geometry textbooks for further examples. See also section 11.2. You will be held responsible for the reading on tests. Do problems 2.2:6-8, 19-21 and 2.3: 9-12.

    6.

    7. Under what circumstances is a conditional true? For every specific case where the antecedent and consquents are true.

    8.

    19. Heather read an ad: "If you want to improve your game, then you'll wear Nyebox Shoes." Heather wants to improve her game. If she believes the ad is true, what will she do?
    She will wear the shoes.

    20.

    21. Consider the antecedent: A person is 14 years old. Write one true and one false conditional with this antecedent. True: If a person is 14 years old, then the person is a teenager. False: If a person is 14 years old, then the person is a freshman.

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