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Math Help - What does this even mean? So confused...

  1. #1
    Junior Member
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    What does this even mean? So confused...

    I am totally stuck on this problem.

    Suppose that A is a subset of V^{*}, where V is an alphabet. Prove or disprove each of these statements.

    a) A \subseteq A^2
    b)  \mbox{If} \ A = A^2, \mbox{then}  \ \lambda \in A
    c) A\{\lambda\} = A
    d) (A^{*})^{*} = A^{*}
    What do all these symbols even mean i.e. *, lambda, etc. and how do I go about in solving these problems? Thank you.
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  2. #2
    Newbie aleph1's Avatar
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    Quote Originally Posted by VENI View Post
    I am totally stuck on this problem.

    Suppose that A is a subset of V^{*}, where V is an alphabet. Prove or disprove each of these statements.

    a) A \subseteq A^2
    b)  \mbox{If} \ A = A^2, \mbox{then} \ \lambda \in A
    c) A\{\lambda\} = A
    d) (A^{*})^{*} = A^{*}
    What do all these symbols even mean i.e. *, lambda, etc. and how do I go about in solving these problems? Thank you.
    I am not sure. Doing a wiki search on "alphabet subset theory" I came up with this.

    Free monoid - Wikipedia, the free encyclopedia

    V^{*} may mean an alphabet set minus the empty string.

    \lambda may be the empty string.

    Guessing, A^2 may be the 2-tuples of elements of A.

    With the above, I further conjucture weakly:

    a) is false. A \ is not a 2-tuple.
    b) is false. A \ is not a 2-tuple. A = A^2 \ does not result in \ \ \lambda \in A
    c) not sure what A\{\lambda\} implies.
    d) is true. Removing the empty string twice from the set A which already does not contain the empty string, is equivalent to removing the empty string once.

    Supply more context on the source of this, for example: title of book, paragraph, section or chapter, or class topic under discussion.
    Last edited by aleph1; April 23rd 2009 at 12:12 PM.
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  3. #3
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    Quote Originally Posted by aleph1 View Post
    I am not sure. Doing a wiki search on "alphabet subset theory" I came up with this.

    Free monoid - Wikipedia, the free encyclopedia

    V^{*} may mean an alphabet set minus the empty string.

    \lambda may be the empty string.

    Guessing, A^2 may be the 2-tuples of elements of A.

    With the above, I further conjucture weakly:

    a) is false. A \ is not a 2-tuple.
    b) is false. A \ is not a 2-tuple. A = A^2 \ does not result in \ \ \lambda \in A
    c) not sure what A\{\lambda\} implies.
    d) is true. Removing the empty string twice from the set A which already does not contain the empty string, is equivalent to removing the empty string once.

    Supply more context on the source of this, for example: title of book, paragraph, section or chapter, or class topic under discussion.
    Thank you for your help. The problem comes from a hand out my professor gave me about finite-state automata.
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