Proof of two statements being equal withe rules of logic How can one prove that $P \to Q$ Is the same thing as $[\text{not } P \text{ or } Q]$. I am guessing I would have to prove that they are the negation of the same thing

$p\to q$ means that: $q$ will be true if $p$ is true.

Therefore $p\to q$, entails that: if $q$ is false, then $p$ cannot be true.

So if $p\to q$ then either $p$ is false or $q$ is true. $$p\to q\implies \
eg p\vee q$$

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Conversely.

$\
eg p\vee q$ means that either $p$ is false or $q$ is true.

Threfore $\
eg p\vee q$ entails: if $p$ is true, then $q$ must be true.

$$\
eg p\vee q\implies p\to q$$

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$$\therefore \qquad p\to q\iff \
eg p\vee q$$