 Suppose you start off with no information about which of the four possible combinations of truth values for \(A\) and \(B\) obtains. You then acquire compelling reason to think that either \(A\) or \(B\) is true. You don’t have any stronger belief about the matter. In particular, you have no firm belief as to whether \(A\) is true or not. You have ruled out line 4. The other possibilities remain open. Then, intuitively, you are justified in inferring that if \({\sim}A, B\). Look at the possibilities for \(A\) and \(B\) on the left. You have eliminated the possibility that both \(A\) and \(B\) are false. So if \(A\) is false, only one possibility remains: \(B\) is true.