I'm really stuck at proving general versions for any propositional formula for example:
I) Use truth table to prove this De Morgan's law $$ \lnot (P \land Q) \equiv \lnot P \lor \lnot Q $$
Which is very simple, we construct truth table and compare the results column, if they are the same they are equivalent
II) Also show the general version $$ \lnot (A \land B) \equiv \lnot A \lor \lnot B $$ of the equivalence holds, for any propositional formula A and B. Hint: it is not possible to use the truth table method here, because A and B are arbitrary formulas
The only way that I know is to assume A or B to be tautologies or contradictions so we can substitute A or B with 1 or 0 and proceed with the truth table. However, that doesn't sound about right and we can't use truth tables as well..