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Math Help - Disprove this set of string.

  1. #1
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    Sep 2011
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    Disprove this set of string.

    Disprove the following: for all non-empty languages A,B,C
    (A o B) ⊆ (A o C) → ( B ⊆ C )

    In other words, exhibits non-empty languages A, B and C such that B ⊆/ C and ( A o B) ⊆ (A o C)

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  2. #2
    MHF Contributor
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    Re: Disprove this set of string.

    Welcome to the forum. You should know that rule #11 in the sticky thread in each forum section asks to show some effort in solving your problem. To start, is o concatenation?

    It is relatively easy to find A, B, C ⊆ {1}* such that A o B = A o C = {1}* and C ⊂ B.
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