 Let \(A\) and \(B\) be two logically independent propositions. The four lines below represent the four incompatible logical possibilities for the truth values of \(A\) and \(B\). “If \(A, B\)”, “If \({\sim}A, B\)” and “If \(A, {\sim}B\)” are interpreted truth-functionally in columns (i)–(iii), and non-truth-functionally (when their antecedents are false) in columns (iv)–(vi). The non-truth-functional interpretation we write “\(A \rightarrow B\)”. “T/F” means both truth values are possible for the corresponding assignment of truth values to \(A\) and \(B\). For instance, line 4, column (iv), represents two possibilities for \(A, B\), If \(A, B\), (F, F, T) and (F, F, F).