I want to know some stuff about translating compound statements to english:For the propositions below:p: You have the flu.q: You miss the final examination.r: You pass the course.I want to know how to translate the following compound proposition to english:1). p or q or r.I tried something like this:You have the flu or you miss the final examination or you pass the course.I was just wondering about the usage of commas.2). (p implies not r) or (q implies not r)I tried something like this:If you have the flu, then you do not pass the course, or if you miss the final examination, then you do not pass the course.Again, I was wondering about the comma usage.Can someone please help?
Propositional logic and connectives(translating to english)
logic;propositional logic
The first thing to say is that in propositional logic every statement will have a truth value.If (P or Q or R) evaluates to True (which it doesn't have to) then a natural English way to translate would be:Either you have the flu, you miss the final examination or you pass the course.Note that this or is clearly inclusive - meaning that it is possible that more than one of those things happens but at least one must. To make that clear beyond doubt in natural English you might structure the sentence using at least. This will be much more long winded but avoids the person you are communicating with thinking that you might mean exclusive or (e.g. the type of or used in true or false - it can be one or the other but not both). If you wanted to account for this you might say something like:At least one of the following is true: you have the flu, you miss the final examination or you pass the course.For your second case what you said is not very natural. You would typically hear someone say:You won't pass the course if you have the flu or miss the final examination.If you are supposed, for whatever reason, to structure the answer as you did, the commas should be removed after your if clauses. This would be better:If you have the flu then you do not pass the course, or if you miss the final examination then you do not pass the course.