I have the following sentence that should be converted into logical connectors:
Either you eat healthy or you will get sick.
One transformation that came into my mind was:
p ---- you do not eat healthy q------ you will get sick
so if I convert into this form:
¬p V q
meaning: you eat healthy or you will get sick, I can convert that into:
p-->q ------- If you do not eat healthy then you will get sick (Form 1)
Also I can do the following:
p---you eat healthy q---you will get sick ¬p--q ------ If you don´t eat healthy then you will get sick (Form 2)
Or by using the XOR and the same structure than Form 2:
p xor q
you eat healthy or you will get sick, and I know that both situations cannot be true or false at the same time (Form 3).
The question that I have is which of these three forms is the correct one for the sentence given. The three truth tables are different and I have specially doubts with the XOR, because when I use the conditional in Forms 2 and 3 and I have two T or two F, then the truth table returns me a value of true; situation that does not happen with the XOR.
So which one is more accurate and if its correct the xor form?