Propositional equivalence. Duality problem.

Question

I recently have started practicing problems on Discrete Mathematics by Keneth H.Rosen. There seems to be an interesting problem on Propositional Equivalence which states that when is $s^{*} = s$. Where s is a compound proposition and $s^{*}$ is the dual of $s$.

Answer 1

One solution I was thinking of is s* = s whenever s* <-> s is a tautology. Correct me if I am wrong.

Looking for suggestions.

Thanks!

Answer 2

If $s$ has any occurrences of $∧,∨, T, or F$, then the process of forming the dual will change it. Then $s^∗=s$ if and only if $s$ is one propositional variable.

N.B: I have recently started learning discrete mathematics and solved this problem a few days ago. :)