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Math Help - Help using logic symbols to rewrite statements

  1. #1
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    Help using logic symbols to rewrite statements

    Hi Everyone.

    I have been given a problem to solve that deals with using logic symbols to rewrite part of a contract. I have an answer that I believe is close to being correct. I would be grateful for any help on understanding my mistakes though. Here is the complete problem (it's long )

    The rules for a certain frequent flyer club include the following statements
    :"Any member who fails to earn any milage during the first twelve months after enrollment in the program may be removed from the program. Except as otherwise provided, any member who fails at any time to earn mileage for a period of three consecutive years is subject to termination of his or her membership and forfeiture of all accrued mileage. Notwithstanding this provision, no pre-July 1, 1993, member who has earned mileage(other than enrollment bonus) prior to July 1, 1994 shall be subject under this provision to the termination of his or her membership and to the cancellation of mileage accrued prior to July 1, 1994, until the amount of such mileage falls below 10,000 miles (the amount of mileage necessary for the lowest available award under the structure in place as of June 30, 1993), or until December 15, 1999, whichever comes first.
    Let x be a particular member of this club, and let
    p="x fails to earn mileage during the first twelve months after enrollment"

    q="x fails to earn mileage for a period of three consecutive years"

    r="x became a member prior to July 1,1993"

    s="x currently has at least 10,000 miles for pre-July 1, 1994 mileage (not included bonus enrollment miles)"

    t="the current date is prior to December 15, 1999"

    Use symbols to write the complete condition under which x's membership may be terminated.

    Okay now that I have typed up the question let me post my answer.

    I got: (p∨q)∨(r∧~s)∨~t

    Thank you in advance
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  2. #2
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    Quote Originally Posted by Twinsfan85 View Post
    Hi Everyone.

    I have been given a problem to solve that deals with using logic symbols to rewrite part of a contract. I have an answer that I believe is close to being correct. I would be grateful for any help on understanding my mistakes though. Here is the complete problem (it's long )

    The rules for a certain frequent flyer club include the following statements
    :"Any member who fails to earn any milage during the first twelve months after enrollment in the program may be removed from the program. Except as otherwise provided, any member who fails at any time to earn mileage for a period of three consecutive years is subject to termination of his or her membership and forfeiture of all accrued mileage. Notwithstanding this provision, no pre-July 1, 1993, member who has earned mileage(other than enrollment bonus) prior to July 1, 1994 shall be subject under this provision to the termination of his or her membership and to the cancellation of mileage accrued prior to July 1, 1994, until the amount of such mileage falls below 10,000 miles (the amount of mileage necessary for the lowest available award under the structure in place as of June 30, 1993), or until December 15, 1999, whichever comes first.
    Let x be a particular member of this club, and let
    p="x fails to earn mileage during the first twelve months after enrollment"

    q="x fails to earn mileage for a period of three consecutive years"

    r="x became a member prior to July 1,1993"

    s="x currently has at least 10,000 miles for pre-July 1, 1994 mileage (not included bonus enrollment miles)"

    t="the current date is prior to December 15, 1999"

    Use symbols to write the complete condition under which x's membership may be terminated.

    Okay now that I have typed up the question let me post my answer.

    I got: (p∨q)∨(r∧~s)∨~t

    Thank you in advance
    The sad part is how realistic the contract reads. I feel as though pure logic has been tainted!

    I get this counterexample to your answer:

    If p is false, q is true, r is true, s is true, and t is true, then x's membership cannot be terminated, but your answer gives true.

    I get

    p v (q ^ (~r v ~s v ~t))
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