Hello, I have a problem in my computer science class that goes as follows:

" prove the following using logical proofs (not truth tables)"

(p --> q) V (p --> r) V p is a tautology

I can get a few steps into it, then get stuck. Please help!

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- Feb 2nd 2010, 12:30 PMtriathleteLogical Equivalence Help
Hello, I have a problem in my computer science class that goes as follows:

" prove the following using logical proofs (not truth tables)"

(p --> q) V (p --> r) V p is a tautology

I can get a few steps into it, then get stuck. Please help! - Feb 2nd 2010, 12:46 PMPlato
$\displaystyle \begin{gathered}

\left( {p \to q} \right) \vee \left( {p \to r} \right) \vee p \hfill \\

\left( {\neg p \vee q} \right) \vee \left( {\neg p \vee r} \right) \vee p \hfill \\

\neg p \vee \left( {q \vee r} \right) \vee p \hfill \\

\left( {\neg p \vee p} \right) \vee \left( {q \vee r} \right) \hfill \\

\end{gathered} $ - Feb 2nd 2010, 01:06 PMnovice
By predicate calculus:

$\displaystyle P$ (hypothesis)

$\displaystyle P\vee (P\rightarrow R)$ (Disjunction Introduction)

$\displaystyle (P\vee (P\rightarrow R))\vee (P\rightarrow Q)$ (Disjunction Introduction and end of proof)