I will buy a car or take a vacation.

Question

I will buy a car or take a vacation. I will buy a car. Therefore, I will not take a vacation

What is this form called? Is it valid or invalid?

I understand the form to be "P or Q. P. Therefore ~Q."

But what is this form called?

Answer 1

This is a form of disjunctive syllogism, or modus tollendo ponens.

Answer 2

You are saying that (P or Q) and P implies not Q. To check if this argument is valid, just set up a truth table (see https://www.math.fsu.edu/~wooland/argumentor/TruthTablesandArgs.html) If you have tautology under the column 【(P or Q) and P 】implies not Q， then the statement if valid. Just check the link to see how to set it up.

Answer 3

This argument is only valid if the 'or' is taken to be an exclusive or. if the 'or' here is an inclusive or, then the argument is not valid: maybe it is possible for you to buy the car and take a vacation. But, it is not unreasonable to assume that you cNnot do both: cars and vacations can both be expensive, and so you may indeed only eb able to afford one of those luxuries.

So, under the assumption that the 'or' is indeed meant as an exclusive disjunction, we can consider this argument to be an example of Exclusion: if two things cannot both be true, but one of them is, then the other has to be false. This is also known as Modus Ponendo Tollens: through the act of positively asserting something, we can deny something else.