How to interpret "$P\,$ but $Q\,$" when symbolizing natural language statements? > If it is wednesday then I won't study, but if it rains then I will study and watch TV Let's make that into propositions: $P:$ It is wednesday $Q:$ I will study $R:$ It rains $S:$ I will watch TV Now let's get the premises in that sentence... here is my problem: I'm not sure what to do with the "but". Would this be right? $P \implies \lnot Q$ $R \implies Q \land S$

What you have isn't quite right. As a hint, a more complete way of expressing your sentence is:

> "If it is Wednesday **and it doesn't rain** then I won't study, but if it rains then I will study and watch TV."