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Math Help - Can you assist me with a few logic questions?

  1. #1
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    Can you assist me with a few logic questions?

    Okay, for my first question, I dont understand how the following statement is equal to the other:


    the statement : (P-->Q)---> ~(~Q-->P)


    is equal to: (P^Q) v (~Q ^~P)


    How?
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  2. #2
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    Hello, doublecheckmyanswerspleas!

    I suspect there's a typo . . .


    I dont understand how the following statement is equal to the other:

    The statement: . (P \to \:{\color{red}\sim}\,Q) \to \;\sim(\sim\!Q \to P)

    is equal to: . (P \wedge Q) \vee (\sim\!Q \:\wedge \sim\!P)

    p \to q \;\equiv \;\sim p \vee q . . I call it ADI (alternate definition of implication).


    \begin{array}{ccccc}<br />
(P \to \:\sim Q)  \; \to \; \sim(\sim\!Q \to P) & & \text{Given} \\ \\<br /> <br />
(\sim\!P \:\vee \sim\!Q) \;\to \;\sim(Q \vee P) & & \text{ADI} \\ \\<br /> <br />
(\sim\!P \:\vee \sim\!Q) \;\to \;(\sim\!Q \:\wedge \sim\!P) & & \text{DeMorgan} \\ \\<br /> <br />
\sim(\sim\!P\:\vee \sim\!Q) \;\vee \;(\sim\!Q \:\wedge \sim\!P) & & \text{ADI} \\ \\<br /> <br />
(P \wedge Q) \;\vee \;(\sim\!Q \:\wedge \sim\!P)& & \text{DeMorgan}<br /> <br /> <br />
\end{array}

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