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Homework Help: Am I understanding this relation?

  1. Dec 4, 2006 #1
    Hello everyone i'm not sure if i'm understanidng this relation.

    The question is:

    Let S be the set of all strings in a's and b's. Define a relation T on S as folows:

    FOr all s, t in S, s T t if and only if t = as. That is, t is the concatenation of a with s.

    c. Is ba T aba?
    I said yes, because aba is the concatneation of a with ba. Thus a + (ba)

    e. Is abb T^-1 bba?

    Well I know this means,
    (abb T^-1 bba) if and only if (bba T abb)

    now abb, can be broken into a + bb, but would that break the rules? like the order odes it have to be the same? So for this one i would say no.



    f. Is abba T^-1 bba?

    this means
    bba T abba
    I would say yes, becuase
    abba is just a + bba


    Any clarification if i'm understanding right?

    Thanks!
     
  2. jcsd
  3. Dec 5, 2006 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Good!

    Yes, that's correct. T-1 is just T reversed. s T-1 t if and only if s is at. abbT-1bba is NOT true because bbaTabb is not true.

    Yes, of course. The same letters in different order are different strings. Nothing in the definition of T or T-1 changes that!



    Good!

     
  4. Dec 5, 2006 #3
    thanks for the help!
     
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