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Discrete Mathematic Question

  1. Sep 15, 2007 #1
    1. The problem statement, all variables and given/known data
    Hi. I need to prove that these 3 eqns are the same.

    [tex]p \rightarrow q \vee r[/tex]

    [tex]p \wedge \neg q \rightarrow r [/tex]

    [tex]p \wedge \neg r \rightarrow q[/tex]


    2. Relevant equations
    [tex]p \rightarrow q \equiv \neg p \wedge q[/tex]

    3. The attempt at a solution

    [tex]p \rightarrow q \vee r[/tex]

    [tex]p \rightarrow \neg q \rightarrow r[/tex]

    [tex]\neg p \wedge \neg q \rightarrow r[/tex]

    That's all I got. Please help me.
     
    Last edited: Sep 16, 2007
  2. jcsd
  3. Sep 16, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I'm not sure what you are doing. I don't see how you got [itex]p \rightarrow \neg q \wedge r[/itex] from any of those!

    Using your "relevant equation", the first becomes [itex]\not p\wedge (q\vee r)[/itex], the second [itex]\not (p\wedge \not q)\vee r[/itex] which is itself equivalent ot [itex](\not p \vee q)\vee r.

    Frankly I would use truth tables!
     
  4. Sep 16, 2007 #3
    I had made a mistake, now I have corrected it. and I am not allowed to use the truth table.

    Thank you
     
  5. Sep 16, 2007 #4
    just ignore this, I need latex for MS word.
    [tex]\sqrt{2 \times (\frac{0.1}{3.2})^2 + (\frac{0.2}{3.0})^2}[/tex]

    [tex]=0.079984804cm^3[/tex]

    [tex]=0.08cm^3[/tex]
     
    Last edited: Sep 16, 2007
  6. Oct 17, 2007 #5
    Again, please ignore this
    just ignore this, I need latex for MS word.
    [tex]\frac{\Delta v}{v} = \sqrt{(\frac{\Delta \ell}{\ell})^2 + (\frac{\Delta t}{t})^2}[/tex]

    [tex]\frac{\Delta v}{v} = \sqrt{(\frac{0.001}{0.101})^2 + (\frac{0.00001}{0.3950})^2}[/tex]

    [tex]\frac{\Delta v}{v} = 0.0099m/s[/tex]

    [tex]\frac{\Delta a}{a} = \sqrt{(\frac{\Delta v_1}{v_1})^2 + (\frac{\Delta v_2}{v_2})^2} + (\frac{\Delta d}{d})^2}[/tex]

    [tex]\frac{\Delta a}{a} = \sqrt{(\frac{0.0099}{0.256})^2 + (\frac{0.0099}{0.620})^2 + (\frac{0.01}{0.60})^2}[/tex]

    [tex]\frac{\Delta a}{a} = \sqrt{(0.00149) + (0.000254) + (0.000277)}[/tex]

    [tex]\frac{\Delta a}{a} = \sqrt{0.002021}[/tex]

    [tex]\frac{\Delta a}{a} = 0.041945[/tex]

    [tex]\frac{\Delta a}{a} = 0.042 m/s^2[/tex]
     
    Last edited: Oct 17, 2007
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