 The same point can be made with negated conjunctions. You discover for sure that \({\sim}(A \amp B)\), but nothing stronger than that. In particular, you don’t know whether \(A\). You rule out line 1, nothing more. You may justifiably infer that if \(A, {\sim}B\). Hook gets this right. In column (iii), if we eliminate line 1, we are left only with cases in which “\(A \supset{\sim}B\)” is true. Arrow gets this wrong. In column (vi), eliminating line 1 leaves open the possibility that “\(A \rightarrow{\sim}B\)” is false.