# Math Help - logic

1. ## logic

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

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

a tautology? Incidentally, what is the translation of this statement back to the language of $\cup, \cup \ and \subset$

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

3. Do you have to get rid of $\wedge$?