I'm trying to learn more about logical statement. I have this question: (q --> -p) --> r. Im supposed to create a combinatorial circuit out of this statement. What i did was to convert the logical statement to something easier. So i got: $(q \rightarrow -p ) \rightarrow r$ ... $(-q \cup -p ) \rightarrow r$...$-(-q \cup -p ) \cup r$ and then i got $(q \cup p ) \cup r $
Im really not sure if this is correct, could anyone please check and correct if I did anything wrong? Thanks!
Up until the last step, your reasoning works. However, we have to use De Morgan’s law to distribute negation over conjunction/disjunction. Instead, we would get: $$ \neg (\neg q \lor \neg p) \lor r \equiv (q \land p) \lor r $$