1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    Yes, you already have two answers which implied that. :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: DISCRETE MATH: Express the following using propositions p,q,r and logical connectives
Loading...