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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 5

    Given p = "This is a frog.", q = "It should croak." Write out in words the following:

  1. Conditional (p=>q).

     

  2. Inverse (~p=>~q).

     

  3. Converse (q=>p).

     

  4. Contrapositive (~q=>~p).

     

  5. Biconditional (p<=>q).

     

  6. (6 points) Write out in words the indicated conditional statements for the following sentence: "If I get my allowance today, I'm going to buy my favorite CD."

    1. Inverse:

    2. Contrapositive:

    3. What can you conclude if you are told, "I bought my favorite CD."?

       

  7. Given a 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 identifying each piece.

     

  8. Give a counterexample of: "Bears are large and dangerous to approach."

     

  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.";

     

  10. Rewrite the sentence into a conditional statement: All squares are rhombi.

     

  11. Write the converse and state if it is true: If you are a driver, then you are at least 16.

     

  12. Write the converse to: "We'll go to the fair if they announce square-dancing over the radio."

     

  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.

     

  14. Given: "If a golfer has won the U.S. Open Tournament, then [s]he is in the major leagues." What can you conclude about these two people? Tiger Woods won the U.S. Open Tournament. Bernhard Langer has not won a U.S. Open Tournament.

     

  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."?

     

  16. Bonus: Express the numbers 8 through 12 in base -3. Use 0, 1, and -1 as your digits. Check out the article Third Base in the Nov./Dec. 2001 issue of American Scientist

     

  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.

     

  18. See section 2.2 of your geometry textbook for further examples. Problems 2.2: 6-8 and 19-21 were assigned in 2000-01.

     

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