# propositional logic: prove or disprove

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• May 14th 2012, 08:59 PM
nehal234
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.
• May 14th 2012, 10:17 PM
Soroban
Re: propositional logic: prove or disprove
Hello, nehal234!

I don't understand your difficulty.

Quote:

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. . Most if it? . . . What does that mean?
But i do no know how to prove or disprove it. . Do you understand what a truth table does?

. . $\displaystyle \begin{array}{|c|c|c||cccccccccccc|} p & q & r & [(p & \to & q) & \wedge & (\sim p & \to & r)] & \to & (q & \vee & r) \\ \hline T&T&T & T&T&T&T&F&T&T&{\color{red}T}&T&T&T \\T&T&F & T&F&T&F&F&T&F&{\color{red}T}&T&T&F \\ T&F&T & T&F&F&F&F&T&T&{\color{red}T}&F&T&T \\ T&F&F & T&F&F&F&F&T&F&{\color{red}T}&F&F&F \\ F&T&T & F&T&T&T&T&T&T&{\color{red}T}&T&T&T \\ F&T&F & F&T&T&F&T&F&F&{\color{red}T}&T&T&F \\ F&F&T & F&T&F&T&T&T&T&{\color{red}T}&F&T&T \\ F&F&F & F&T&F&F&T&F&F&{\color{red}T}&F&F&F \\ \hline &&& 1&2&1&3&1&2&1&4&1&2&1 \end{array}$
• May 15th 2012, 12:05 AM
nehal234
Re: propositional logic: prove or disprove
i see how you have used ⇒ and → to be the same. this makes it clear for me.
thanks