
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 $\displaystyle \cup, \cup \ and \subset$

$\displaystyle \left( {A \subseteq B} \right) \wedge \left( {B \subseteq A} \right) \Leftrightarrow \left( {A = B} \right)$

Do you have to get rid of $\displaystyle \wedge$?