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Math Help - Opinion on proof (cartesian product -sets)-some guidance needed

  1. #1
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    Opinion on proof (cartesian product -sets)-some guidance needed

    Good day to all

    I have attached the question asked and my work for better legibility. I need to prove that the LHS is a proper subset of the RHS. I have (I believe) managed to proved that it is a subset of the RHS but not a proper subset. I know that to do so, I would need to prove that the LHS subset of RHS and LHS different than RHS. This is where my problem arises. Any help would be greatly appreciated.

    Kindest regards
    Attached Thumbnails Attached Thumbnails Opinion on proof (cartesian product -sets)-some guidance needed-question2.jpg  
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  2. #2
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    Why not learn to post in LaTeX?
    It almost as easy as equation editor.
    [tex](a,b)\in A\times B[/tex] gives  (a,b)\in A\times B .

    You work is correct.
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  3. #3
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    I am not sure if in general this is a proper subset because each of the implication (except for the last) can be turned into an equivalence...
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  4. #4
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    Quote Originally Posted by emakarov View Post
    I am not sure if in general this is a proper subset because each of the implication (except for the last) can be turned into an equivalence...
    I took that to be a typo: lack of LaTex usage.
    Because clearly it need not be a proper subset.
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