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Homework Help: DISCRETE MATH: Express the following using propositions p,q,r and logical connectives

  1. Jan 9, 2007 #1
    1. The problem statement, all variables and given/known data

    Express the system specifications using the propositions p "The user enters a valid password," q "Access is granted," and r "The user has paid the subscription fee" and logical connectives.

    a) The user has paid the subscription fee, but does not enter a valid password.

    b) Access is granted whenever the user has paid the subscription fee and enters a valid password.

    c) Access is denied if the user has not paid the subscription fee.

    d) If the user has not entered a valid password but has paid the subscription fee, then access is granted.

    2. Relevant equations

    p = "The user enters a valid password"
    q = "Access is granted"
    r = "The user has paid the subscription fee"


    3. The attempt at a solution

    a) [tex]r\,\wedge\,\neg\,p[/tex]

    b) [tex]q\,\longleftrightarrow\,(r\,\wedge\,q)[/tex]

    c) [tex]\neg\,r\,\longrightarrow\,\neg\,q[/tex]

    d) [tex](\neg\,p\,\wedge\,r)\,\longrightarrow\,q[/tex]


    Do these answers look right?
     
  2. jcsd
  3. Jan 9, 2007 #2

    radou

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    Everything looks right, except you made a typo (I guess) in b), it should be [tex]q\,\longleftrightarrow\,(r\,\wedge\,p)[/tex], unless I'm missing something.
     
  4. Jan 9, 2007 #3

    matt grime

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    Even modulo typos, b is not right. The implication is not both ways. It does not assert that the only way to get access is with subscription and a valid password.
     
  5. Jan 9, 2007 #4

    radou

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    Excuse my mistake, it should be [tex](r \wedge p) \Rightarrow q[/tex].
     
  6. Jan 9, 2007 #5
    So they are all right except that B is really [tex](r\,\wedge\,p)\,\longrightarrow\,q[/tex]?
     
  7. Jan 10, 2007 #6

    radou

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    Yes, you already have two answers which implied that. :wink:
     
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