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I just need my solution checked since I'm not sure if it's valid, especially the final statement

Question:

Show $p \Rightarrow (\neg(q \land \neg p))$ is a tautology by assuming:

$u \Rightarrow v$ is logically equivalent to $\neg u \lor v$

My solution:

$\neg(q \land \neg p))$ is logically equivalent to $\neg q \lor p$ (by De Morgan's law),

so $\neg q \lor p$ is logically equivalent to $q \Rightarrow p$ (given by the question) hence $p \Rightarrow (q \Rightarrow p)$ and therefore $p$ is a tautology?

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    $p \Rightarrow (\neg(q \wedge \neg p)) \equiv \neg p \vee \neg q \vee p \equiv \neg p \vee p \vee q \equiv 1 \vee q \equiv 1$2011-04-27
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    Couldn't you just write down the truth table and check that it's always true?2011-04-27
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    Josh, yes, but that would be the longest way to answer the question, besides this particular question asks us to solve it using the hint given2011-05-01
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    by the way, user4143 I think you made a mistake on the last 2 statements, I believe it's meant to be $\lnot q$, prob a typo?2011-05-01
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    I think the title is inaccurate. You are not asking us to show this is a tautology, which in this case is easily done with a truth table. Instead, you are asking us to check your homework answer for you.2011-05-02

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