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Need practice problems help

  1. Jul 21, 2005 #1
    I have about 10 questions, I hope someone can take the time to help me with. The directions are: "Use the 18 rules of inference, supply a proof for each of the following arguments." So, here goes:

    1.) 1. (R v X) > (A > B)
    2. ~ Q > ~ C
    3. ~ C > Z
    4. R .Y
    5. Q v A /Z v B

    2.) 1. E . (P . B)
    2. (E . B) >~ (P.~M) /E.M

    3.) 1. ~(S v C)
    2. ~(S . R) > (C v D) /D

    4.) 1. D > P /(I . D) > P

    5.) 1. P v (Y . H)
    2. (P v Y) >~ (H v C)
    3. (P .~ C) > (K . X) /X v T

    6.) 1. A = J
    2. A v J
    3. A > (J > W) /W

    7.) 1. ~Q> (C . B)
    2. ~T> (B . H)
    3. ~(Q . T) /B

    8.) 1. (U . P) >Q
    2. ~ O > U
    3. ~ P > O
    4. ~ O . T /Q

    9.) 1. (J>K) . (~O>~P)
    2. (L > J) . (~M>~O)
    3. ~K> (L v~ M)
    4. ~K . G /~P

    10.) 1. (F . M) > (S v T)
    2. (~S v A) > F
    3. (~S v B) > M
    4. ~S . G /T

    Okay, that's all the questions. Now here is the legend key:
    / separates what the conclusion is supposed to be.
    . conjunction
    v disjunction
    > implication
    = biconditional
    ~ negation

    This is for an introductory to logic class. I hope someone can help. Thank you.
     
  2. jcsd
  3. Jul 21, 2005 #2

    honestrosewater

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    Gold Member

    I read that as:
    1. (R v X) > (A > B)
    2. (~ Q) > (~ C)
    3. (~ C) > Z
    4. R .Y
    5. Q v A
    C. Z v B
    By my calculations, this argument is invalid. Counterexample: (R, Y, C, Q) are true and (Z, B, A) are false (X is true or false). Did you copy it correctly? How are you grouping negations?
     
  4. Jul 21, 2005 #3

    honestrosewater

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    Gold Member

    Here are some hints for the next three to get you started.
    2) Can you derive ~(P . ~M)?
    3) Can you derive (~S v ~R)?
    4) Do you have the rule: ((P . Q) > R) = (P > (Q > R))?
     
  5. Jul 21, 2005 #4
    Re: Re: Practice Problems Help

    Yes I did copy it correctly. This is directly from my teacher, too. I don't think he feels it's invalid. And, the ones that you put parentheses around, he didn't. I don't know if that matters or not. I really don't get anything about this class at all. As far as how am I grouping negations, I have no idea on that either. Thanks.
     
  6. Jul 21, 2005 #5

    honestrosewater

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    Gold Member

    Well, regardless of what he may feel, I checked it again, and it is invalid. Do you know how to check an argument for validity?
    I added the parentheses to make clear what was being negated.
    If you have no idea what you're doing, there isn't much I can do for you today. If you have a problem understanding something specific, I'll try to help. But we don't do people's homework for them here, so you'll have to put in some effort.
     
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