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Math Help - Propostions true, false, unknown

  1. #1
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    Propostions true, false, unknown

    I am studying for an exam next week and looking over several old tests which I have the answers to. Our instructor barely touched on unknown status of variables nor did the book. So, I am hoping to write my reasoning for these and see if I am on the right track.

    Thanks for all you folks who get this and are willing to help the confused.

    p is true q is true r is false status of s is unknown

    evaluate r--> (s ^ q)

    I reasoned that since r is false the statement is true by default which matches the answer I have from the instructor.


    evaluate s <---> (r-->s)

    Since this statement can only be true if and only if and we do not know the status of s we can not determine whether it is true or false and so it is unknown. Again, I know this is the answer but is my logic sound?

    evaluate ~(s^r)

    I don't understand how we can say true on this one. r is false and so not r is true but the status of s is unknown and there is an and here!!! If there was an or between these I would h ave no problem saying that this state ment is true. Please explain.

    Evaluate (p--> q) <--> ~(r or s)

    Why is this unknown???? We know p and q are true and that r is false and r and s are connected by an or so if either is correct then the statement should be!!!! This one really confuses me. Is it that if and only if requires all to be known even if the statement involved with the if and only if has an or clause in it???? PLease explain.
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  2. #2
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    Quote Originally Posted by frostking2 View Post
    p is true q is true r is false status of s is unknown
    evaluate r--> (s ^ q)
    evaluate s <---> (r-->s)
    evaluate ~(s^r)
    Evaluate (p--> q) <--> ~(r or s)
    Here are two favorite sentences of logicians.
    A false statement implies any statement.
    A true statement is implied by any statement.

    1. r--> (s ^ q) is true by the first saying.

    2. s <---> (r-->s) is false because (r-->s) is true but we donít know about s.

    3. ~(s^r)=(~sv~r), ~r is true so (~sv~r) is true.

    4. You do this one.
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  3. #3
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    Thanks again for your help Plato. Have a great weekend.
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