# logic

• Nov 2nd 2008, 06:34 AM
Showcase_22
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 $\cup, \cup \ and \subset$
• Nov 2nd 2008, 09:15 AM
Plato
$\left( {A \subseteq B} \right) \wedge \left( {B \subseteq A} \right) \Leftrightarrow \left( {A = B} \right)$
• Nov 3rd 2008, 12:53 AM
Showcase_22
Do you have to get rid of $\wedge$?