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I'd like to provide an attempt, but all I can think off is trying to construct one of the following complete set of boolean functions and have been unsucessful in that. I can only get an additional function: $1$. $0 \leftrightarrow 0 \equiv 1$ (some) sets that, are functional complete: $\{\wedge, \vee, \neg \}, \{\vee, \neg \}, \{\wedge, \neg \}, \{\rightarrow, \neg \} , \{\rightarrow, 0 \}, \{NAND\}$

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    $\begingroup$ Try to use the existing connectives to reproduce a complete one, like $\{ \to, \lnot \}$. Hint: $A \leftrightarrow 0 \equiv \lnot A$ $\endgroup$
    – Mauro ALLEGRANZA
    Commented Jan 26, 2022 at 14:50

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