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Math Help - recursive definition

  1. #1
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    Sep 2008
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    Question recursive definition

    Hi
    I have a problem which i couldn't solve
    could somebody help me

    1. Give a recursive definition of the length of a well formed formula, that is of the number of symbols occuring in it . for example the length of (p ^ (q)) is 8.


    2. show that there is no well formed formula of length 2,3 and 6 , but any other positive length is possible

    Please respond as soon as possible
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  2. #2
    Member
    Joined
    Aug 2008
    Posts
    80
    Hello,

    1) The length of an atom is 1.
    2)a) If the length of w is n, the length of (w) is n+2.
    2)b) If the length of w_1 is n_1 and the length of w_2 is n_2, the length of w_1^2w_2 is n_1+n_2+1.
    2)c)...etc.

    For the second problem, use the results of the first one.

    Bye.
    Last edited by wisterville; September 21st 2008 at 09:53 PM. Reason: Rewrote the base case in 1).
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