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Math Help - Propositional

  1. #1
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    Propositional

    a propositional p is given with p :If christmas lasts to easter, I get more presents.

    a) Form the negation to the propositional p

    b) Form the contrapositive form to the propositional.

    ________________________________________________


    a) If christmas won't last to easter, I won't get more presents ..

    b) Christmas lasts to easter, so I will get more presents..

    Is anyone of that even slightly right, I missed a few classes so I don't know that much sadly =/
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by greensnake View Post
    a propositional p is given with p :If christmas lasts to easter, I get more presents.

    a) Form the negation to the propositional p

    b) Form the contrapositive form to the propositional.

    ________________________________________________


    a) If christmas won't last to easter, I won't get more presents ..

    b) Christmas lasts to easter, so I will get more presents..

    Is anyone of that even slightly right, I missed a few classes so I don't know that much sadly =/
    Those are incorrect i'm afraid. Here's how to go about this


    Let P and Q be statements.

    We call the statement: "If P, then Q" an "implication," and often write it as shorthand using the following logical symbols: " P \implies Q"

    The contrapositive of P \implies Q is ( \neg Q) \implies ( \neg P)

    When we are negating an implication, we use the fact that:

    P \implies Q \equiv ( \neg P) \vee Q

    So the negation of P \implies Q is \neg (P \implies Q) = \neg ( ( \neg P) \vee Q) \equiv P \wedge ( \neg Q) by DeMorgan's Laws.

    Note: the \neg symbol means "not." So, for instance, \neg P means "not P"



    you may want to see here, they don't have symbols, but the explanations are ok.


    Now, do you think you can continue?
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  3. #3
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    Ok, I think I got some of it.

    So,

    a) Christmas lasts to easter, I won't get any more presents.

    b) I won't get anymore presents, so Christmas won't last to easter.

    I think b) is right, but not too sure about a) (negation)

    Great link btw
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