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I mean simplifying a wff(well-formed formula)in which, only $\lor$, $\land$, $()$and $\lnot$ are allowed, as minimizing the occurence of connective symbols( $\land$ and $\lor$).

It's self-evident that there is no need to further simplifying wffs in which each variable only occurs once, say $A \lor B \land C$.

But it seems to me some other cases, like $(\lnot A_1 \land \lnot A_2) \lor(\lnot A_1 \land \lnot A_3) \lor(\lnot A_2 \land \lnot A_3) $ can't be simplified either.

My question is what is the rule determining whether a wff can be simplified?

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    Not an answer, but mildly apropos. In logic design, a broad goal used to be to minimize the number of operators ($\land, \lor$, etc.) involved in a wff as these were 'expensive'. Nowadays, design focuses more on reducing the 'depth' of a wff as speed is more of an issue. Simplicity is in the eye of the beholder.2012-12-21

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