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Math Help - Proof by induction method

  1. #1
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    Proof by induction method

    Hi!

    Can someone explain me the way to do this exercise?

    The exercise say's:

    Consider the alphabet \Sigma=\{a,b\} and the languages \Gamma and \Delta defined inductively with the following rules:

    Proof that \Gamma = \Delta

    \Gamma is:

    (i) \epsilon\in\Gamma

    (ii)\mbox{ If } \alpha\in\Gamma \Rightarrow \alpha a\in\Gamma

    (iii)\mbox{ If }\alpha\in\Gamma \Rightarrow \alpha b\in\Gamma

    \Delta is:

    (i)\epsilon\in\Delta

    (ii)\mbox{ If }\alpha\in\Delta \Rightarrow a\alpha\in\Delta

    (iii)\mbox{ If }\alpha\in\Delta \Rightarrow b\alpha\in\Delta

    Thank's
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  2. #2
    MHF Contributor
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    May I ask, what have you tried and where are you stuck?
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