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Math Help - logic notation

  1. #1
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    Aug 2008
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    logic notation

    Hello,

    I'm working on this assignment that is due in 2 hours, and I'm not quite sure about these two questions that I have yet to complete before I can submit this assignment.

    1. Give the reasons for each of the steps provided to validate the argument

    [(P → Q) /\ (R \/ S) /\ (P \/ R)] → (Q → S)

    Step:

    a) (Q → S)
    b) Q /\ S
    c) S
    d) R \/ S
    e) R
    f) P → Q
    g) Q
    h) P
    i) P \/ R
    j) R
    k) R /\ R
    l) therefore Q → S

    2. Find the value of the Boolean expression

    (wz + yx' + wy')(y'x + zx') + ( (w + y)(x' + y) )'

    if

    a) w = x = 0 and y = z = 1
    b) w = y = 1 and x = z = 0

    I shall review this material after I submit the assignment and will learn and understand it better. Right now, I just really need to get this handed in. Any help would be much appreciated.

    Thank you kindly!
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  2. #2
    Super Member

    Joined
    May 2006
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    Lexington, MA (USA)
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    Hello, spider_dude!

    1. Give the reasons for each of the steps provided to validate the argument

    \bigg[(P \to Q) \wedge (\sim\! R \vee S) \wedge (P \vee R)\bigg] \to (\sim\! Q \to S)

    \begin{array}{ccc}<br />
(P \to Q) \wedge (S\:\vee \sim\! R) \wedge (R \vee P) & & \vee\text{ is commutative} \\ \\<br />
(P\to Q) \wedge (\sim\! S \to \sim\! R) \wedge ( \sim R\! \to P) & & \text{de{f<br />
}. of implication} \\ \\<br />
(\sim\! S \to\sim\! R) \wedge (\sim\! R\to P) \wedge (P \to Q) & & \wedge\text{ is assoc. \& comm.} \\ \\<br />
\sim\!S \to Q & & \text{syllogism} \\ \\<br />
\sim\!Q\to S & & \text{contrapositive}<br />
\end{array}

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