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Math Help - Pleaseeee Helppp! I dont solve it

  1. #1
    Junior Member mathemanyak's Avatar
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    Pleaseeee Helppp! I dont solve it

    Let G be a group and Let A,B<=G
    |A|+|B|>G
    Show that G=AB
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  2. #2
    MHF Contributor

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    Quote Originally Posted by mathemanyak View Post
    Let G be a group and Let A,B<=G
    |A|+|B|>G
    Show that G=AB
    we only need to prove that \forall g \in G: \ A \cap gB \neq \emptyset. so suppose, on the contrary, that \exists g \in G: \ A \cap gB = \emptyset.

    then: |G| \geq |A \cup gB|=|A|+|gB|=|A|+|B| > |G|, which is impossible! Q.E.D.
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  3. #3
    Junior Member mathemanyak's Avatar
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    but

    but A and B subgorup
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