Question

Consider the following text "Our agreement states that either no crashes will occur in 2018’s first quarter or the average response time of requests is under an hour. If the agreement is broken, you will pay $8000 in damages. As shown in these records, the average response time is over two hours. You have paid us $8000. I can only conclude that a crash, or multiple crashes, have occurred."
Represent the propositions and the conclusion, clearly labeling propositional atoms (e.g., what is p?). Prove the argument or show that it is incorrect.

Answer 1

A proposition or statement is a sentence which is either true or false while a conclusion is derived from these propositions.

Here, agreement states that:

Let proposition P: No crashes will occur in 2018’s first quarter

Let proposition Q: The average response time of requests is under an hour

If either P or Q is false, the agreement is broken and you need to pay $8000.

Since, it is given that the average response time is over two hours, i.e., Q is false, the agreement is broken and you need to pay $8000.

Here, conclusion is: a crash, or multiple crashes, have occurred (i.e., P is false).

Clearly the conclusion is invalid since the average response time is over two hours (i.e. Q is false) but we can not say that at least one crash has happened (i.e. we can't say that P is false).