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Math Help - Derivation rules

  1. #1
    Newbie
    Joined
    Jan 2011
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    Post Derivation rules

    Hello,

    I have recently started this course and I believe it is the beginner course. At my school it is labeled CSC 221.

    I am currently working on a homework assignment and I am having a little bit of trouble.

    The problem states:
    Assuming all of the following are correct.

    Processor B is not working and processor C is working.
    Processor A is working if and only if processor B is working.
    At least one of the two professors A, B is not working.



    Let a = “A is working”, b = “B is working” and c = “C is working”.



    a. Write each status report in terms of a, b, and c, using the symbols of formal logic.


    ¬b ^ c
    a→ b
    ¬a ¬b

    b. How would you justify the conclusion that B is not working? (In other words, given
    the statements in part (a), which derivation rule allows you to conclude ¬b)

    part b I am having difficultly finding what exact rule it is looking for. I don't understand all the rule completely which is making it a little difficult specially with all these new concepts being thrown at me at one time. Some are self explanatory others I am unsure.

    If b is not working then c is working but a is not. therefore the only working processor would be c. That is what I get if be is not working. But I don't know how to write that down. or what rule I use to logically prove that.

    Thanks
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  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by Newskin01 View Post
    Hello,

    I have recently started this course and I believe it is the beginner course. At my school it is labeled CSC 221.

    I am currently working on a homework assignment and I am having a little bit of trouble.

    The problem states:
    Assuming all of the following are correct.

    Processor B is not working and processor C is working.
    Processor A is working if and only if processor B is working.
    At least one of the two professors A, B is not working.



    Let a = “A is working”, b = “B is working” and c = “C is working”.



    a. Write each status report in terms of a, b, and c, using the symbols of formal logic.


    ¬b ^ c
    a→ b
    ¬a ¬b

    b. How would you justify the conclusion that B is not working? (In other words, given
    the statements in part (a), which derivation rule allows you to conclude ¬b)

    part b I am having difficultly finding what exact rule it is looking for. I don't understand all the rule completely which is making it a little difficult specially with all these new concepts being thrown at me at one time. Some are self explanatory others I am unsure.

    If b is not working then c is working but a is not. therefore the only working processor would be c. That is what I get if be is not working. But I don't know how to write that down. or what rule I use to logically prove that.

    Thanks


    Part (a) is incorrect: line 2 must be a\leftrightarrow b

    As for part (b): from line 1 in part (a) it follows at once that \neg b

    Tonio
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