how to make Propositional logic from several claims.

Question

i'm having issues connecting the dots in order to create a main claim.

if a sentence says, i will fly only if the plane arrived. let's say that $P =$ plane arrived, $Q =$ i will fly.

so the sentence is $P\rightarrow Q ?$
thank you

Answer 1

i will fly only if the plane arrived.

If this is true, then it means that if plane arrive, I could fly. But there’s no guarantee! However, we do know that if the plane arrive, then I must fly. So here’s how we can diagram it:

fly $\rightarrow$ plane arrived

Answer 2

Using contraposition could be helpfull.

The contrapositive of : X --> Y is ~Y --> ~ X. This is an equivalence.

" I will fly only if plane arrived" means :

"if plane did NOT arrive, then I will NOT fly".

Using contraposition, this is equivalent to :

" If I fly then plane arrived".

Also, remember, " only if " means " necessary condition, and the necessary condition is always after the arrow.