# Thread: laws of propositional logic to simplify

1. ## laws of propositional logic to simplify

[(p ∨ q) =⇒ r] =⇒ (q ∧ r)

I got stuck after using implication and demorgan laws.

2. ## Re: laws of propositional logic to simplify

Originally Posted by Dukeham
[(p ∨ q) =⇒ r] =⇒ (q ∧ r)
I got stuck after using implication and demorgan laws.
We do not know the system names you are to use. Therefore you must fill in the justifications.
$\begin{gathered} (p \vee q) \Rightarrow \;r \hfill \\ \neg (p \vee \;q) \vee \;r \hfill \\ (\neg p \wedge \neg q) \vee \;r \hfill \\ (\neg p \vee r) \wedge (\neg q \vee r) \hfill \\ (\neg q \vee r) \hfill \\ q \Rightarrow \;r \hfill \\ \hfill \\ \end{gathered}$