Let's suppose $\text{S = A + B}$
Dual of $\text{S}$ is $\text{S}_d = \text{A} \cdot \text{B}$
Dual of $\text{S}_d$ is $(\text{S}_d)_d = \text{A + B = S}$
If $\text{S}_d$ is a dual of $\text{S}$ then $(\text{S}_d)_d \Leftrightarrow \text{S}$
$\textbf{NOTE:}$ The dual of the compound proposition that contains only the logical operators $∧, ∨, \sim$ is the proposition obtained by replacing each $∨, ∧,$ by each $∧, ∨.$ Each $\text{T}$ by $\text{F}$ and each $\text{F}$ by $\text{T}.$ But negation remains unchanged.