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Thread: logic

  1. #1
    Super Member Showcase_22's Avatar
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    logic

    Assuming we don't change the meaning (or truth table) of $\displaystyle \Leftrightarrow$, is it true that the truth table for $\displaystyle \Rightarrow$ is the only one which makes:

    $\displaystyle ((a \Rightarrow b) \land (b \Rightarrow a)) \Leftrightarrow (a \Leftrightarrow b)$

    a tautology? Incidentally, what is the translation of this statement back to the language of $\displaystyle \cup, \cup \ and \subset$
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  2. #2
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    $\displaystyle \left( {A \subseteq B} \right) \wedge \left( {B \subseteq A} \right) \Leftrightarrow \left( {A = B} \right)$
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  3. #3
    Super Member Showcase_22's Avatar
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    Do you have to get rid of $\displaystyle \wedge$?
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