Formalising compound sentences in truth-functional logic. I have the sentence: > "If it's the case that if the Butler was guilty then the Chambermaid was guilty then it's not the case that the Butler was guilty but the Chambermaid wasn't." This needs to be formalised in truth-functional logic. Let: > p: the Butler was guilty > > q: the Chambermaid was guilty Would this be formalised in the following manner: > (p → q) → ¬ (p & ¬ q) Thank you for your help.

You've missed a negation. Your sentence translates as "If (If the Butler was guilty then the Chambermaid was guilty) then it isn't the case that (the Butler was guilty and the Chambermaid was guilty)". In other words, you've changed the "wasn't" at the end of your target sentence into "was, too".