# When does the dual of $s =s$?

Why I believe this is not a duplicate: This question might be the same, but the accepted answer is only a partial answer, because it gives no reason as to why those are the only solutions. Since the answer is accepted, that question will likely not receive any further answers. I would like to reopen this question in order to place a bounty and hopefully get a more complete answer.

When does $s^*=s$?

$s^*$ represents the dual of $s$, where $s$ is a compound proposition involving only $T, F, \wedge, \vee, \neg$, and $s^*$ is obtained by interchanging $T$ for $F$, $F$ for $T$, $\wedge$ for $\vee$, and $\vee$ for $\wedge$.