This is a rather simple question but I just want to confirm.
Provided I am given the statements
- $p$: It is cold
- $q$: It is snowing
How would I write an expression to represent
It is false that it is cold or snowing?
Do I simply put the negation outside the statement so it would be $\neg(p \vee q)$ is this always the case...? I was just a little confused because if I distribute the negation it would become $\neg p \wedge \neg q$ and I don't know if that would be logically equivalent?
Yup you are correct, for your sentence, it is $\neg (P \vee Q)$
If you construct a truth table you can see that $\neg (P \vee Q) $ and $(\neg P \wedge \neg Q)$ are equivalent. Can you do that?