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Numbers and Their Application to Math and Science

Odd Solutions for HW Numbers Lesson 6

  1. Determine whether each argument is valid or invalid. If invalid, determine the error in reasoning.
    1. If I inherit $1000, I will buy you a cookie. I inherit $1000. Therefore, I will buy you a cookie.

      A. valid.

    2. All cats are animals. This is not an animal. Therefore, this is not a cat.

      A. valid.

  3. Form a valid conclusion from the following statements.
    1. If I am tired, then I cannot finish my homework. If I understand the material, then I can finish my homework.

      A.The second sentence can be rewritten: If I cannot finish my homework, then I cannot understand the material. Thus by transitive property:
      If I am tired, then I cannot understand the material.

    2. Everyone who is sane can do logic. No lunatics are fit to serve on a jury. None of your sons can do logic.

    A. The first statement rewritten: Everyone who cannot do logic is not sane. Thus by transitive property: None of your sons are fit to serve on a jury.

  5. Help Keith find the sugar addict. Make a truth table from the following statements:
    Keith: Three of you are always right. Who took one of my oatmeal pie cookies?
    Aurora: It was either Rita or Shirleen.
    Rita: Neither Jenny nor I took it.
    Shirleen: Both of you are wrong.
    Jamie: No, one is wrong; the other is right.
    Jenny: No, Jamie, that's not right.

    A. In the table below, JE = ~JA, S = (~A and ~R), JA = (A and ~R) or (~A and R). In the column, what the person says must match to who they are saying took the oatmeal pie cookie. Keith says that three people are saying the truth. Shirleen must have done it because three people testified it was her.
    WHODUNITARSJAJE
    A did it01010
    R did it10010
    S did it11001
    JA did it01010
    Je did it00101

  7. Construct a truth table for [(p|q) ^ ~r] ^ r.
    pqrp|q~r(p|q) ^ ~r [(p|q) ^ ~r] ^ r
    001101
    011010
    100100
    110000

  8.  

    For the next four questions: When I was coming from St. Ives, I meet a man with 7 wives. Each wife had 7 sacks. Each sack had 7 cats. Each cat had 7 kits. Kits, cats, sacks, and wives, how many were going to St. Ives.

  9. Express this quantity in base seven.
    Answer: 111117, because
    kitscatssackswivesman
    77771
  10.  

  11. Convert the base 7 quantity to base 10.
    Answer: 7•7•7•7 + 7•7•7 + 7•7 + 7 + 1 = 2801

  12.  

  13. Multiply and simplify: (2a + 1)(4a - 3) = 8a2 - 2a - 3

  15. Read sections 2.3. Do problems 2.3: 9-12.

    1. Answer: If a polygon has four sides, then it is a quadrilateral. If a polygon is a quadrilateral, then it has four sides.

    3. Answer: a 4' × 5' rectangle

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