How to write a biconditional negative statement in if-then form

Question

I have a statement

Either it's not Saturday or I have to go to work

that I want to write in if-then (conditional statement) form.

I know that

$-p V q ≡ p → q$

So I identified the propositions as such:

p = it's not Saturday

q= I have to go to work

and this would give me

if it's not Saturday then I have to go to work

My confusion is this: the statement "It's not Saturday" is already negated in its ENGLISH form.

It is correct to say p = It's not Saturday or should it be -p = It's not Saturday?

I'm getting really confused between when the English statement is already negated.

Answer 1

Instead, let $P$ = "It's Saturday".

Then, letting $Q$ = "I have to go to work", the given statement is $$\lnot P \lor Q$$ which is equivalent to $$P \rightarrow Q$$ or in words, "If it's Saturday, then I have to go to work".

Answer 2

As you said, you might want to define -

$p ≡ $ It's sunday

$q ≡ $ I have to go to work

And then we'll have - $\lnot p \lor q ≡ p \rightarrow q$.

If it's sunday ($p ≡ T$) - $T \rightarrow Q ≡ T \iff Q ≡ T$

If it's not sunday ($p ≡ F$) - $F \rightarrow Q ≡ T$ ("I can do whatever i want")

If i have to go to work ($Q ≡ T$) - $p \rightarrow T ≡ T \iff p ≡ T$ (it's sunday)

If i don't have to go to work ($Q ≡ F$) - $p \rightarrow F ≡ T \iff p ≡ F$ (it's not sunday)