# Math Help - propositional logic: prove or disprove

1. ## propositional logic: prove or disprove

i'm supposed to prove (p → q) ∧ (¬p → r) ⇒ (q ∨ r) with a truth table and im stuck. i've created most of the truth table by hand. but i do no know how to prove or disprove it.
any help is much appreciated.

2. ## Re: propositional logic: prove or disprove

Hello, nehal234!

. . $\begin{array}{|c|c|c||cccccccccccc|} p & q & r & [(p & \to & q) & \wedge & (\sim p & \to & r)] & \to & (q & \vee & r) \\ \hline T&T&T & T&T&T&T&F&T&T&{\color{red}T}&T&T&T \\T&T&F & T&F&T&F&F&T&F&{\color{red}T}&T&T&F \\ T&F&T & T&F&F&F&F&T&T&{\color{red}T}&F&T&T \\ T&F&F & T&F&F&F&F&T&F&{\color{red}T}&F&F&F \\ F&T&T & F&T&T&T&T&T&T&{\color{red}T}&T&T&T \\ F&T&F & F&T&T&F&T&F&F&{\color{red}T}&T&T&F \\ F&F&T & F&T&F&T&T&T&T&{\color{red}T}&F&T&T \\ F&F&F & F&T&F&F&T&F&F&{\color{red}T}&F&F&F \\ \hline &&& 1&2&1&3&1&2&1&4&1&2&1 \end{array}$