Show that given logical proposition is tautology
$((A \implies C) \land (B \implies C) \land \lnot C) \implies \lnot (A \lor B) $
- I can apply the implication rule first and got
$\lnot((A \implies C) \land (B \implies C) \land \lnot C) \lor \lnot (A \lor B) $
- I applied the implication rule again and got
$ \lnot (( \lnot A \lor C) \land ( \lnot B \lor C) \land \lnot C) \lor \lnot (A \lor B) $
At this point I cannot move any further.
I know that I need to apply somewhere De Morgan's rule and distributivity. Any suggestions?