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Math Help - please help me with my logics h.w

  1. #1
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    please help me with my logics h.w

    hello

    they ask me to find the values for this statement
    (~pvq) -> (pv~q)

    for this stament I got as answer 3 true values and 1 false values, is that right?

    they also ask me to find out whether this stament is a tautology

    [(p->~q)^q]->~p

    i got as answer that this is not a tautology

    finally they ask me to by using morgan laws translate the following statement into a statement that means the same thing.

    The exam was easy and I studied all night.
    my answer is
    I studied all night then the exam was easy.

    thank you.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jhonwashington View Post
    hello

    they ask me to find the values for this statement
    (~pvq) -> (pv~q)

    for this stament I got as answer 3 true values and 1 false values, is that right?
    yes, you're right


    they also ask me to find out whether this stament is a tautology

    [(p->~q)^q]->~p

    i got as answer that this is not a tautology
    right again


    finally they ask me to by using morgan laws translate the following statement into a statement that means the same thing.

    The exam was easy and I studied all night.
    my answer is
    I studied all night then the exam was easy.
    you were doing so well, but this is incorrect.

    recall what DeMorgan's Laws say, there are two of them (that I know of):

    Law 1: \sim (P \wedge Q) \Longleftrightarrow \sim P \vee \sim Q

    Law 2: \sim (P \vee Q) \Longleftrightarrow \sim P \wedge \sim Q



    The statement we have is of the form \sim P \wedge \sim Q

    That is,

    \sim P = "The exam was easy"

    \sim Q = "I studied all night"

    So then,

    P = "The exam was hard" or if you want to be technical, "The exam was not easy"

    Q = "I did not study all night"


    So, the answer you are looking for is:

    \sim (P \vee Q) = "It is not true that the exam was hard or that I did not study all night"
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  3. #3
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    Jhevon, thanks a lot for the help!
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