 One feature of LP which requires some attention is that in LP modus ponens comes out to be invalid. For if \(p\) is both true and false but \(q\) false (only), then \(p \supset q\) is both true and false and hence is designated. So both \(p\) and \(p \supset q\) are designated, yet the conclusion \(q\) is not. Hence modus ponens for \(\supset\) is invalid in LP. (One way to rectify the problem is to add an appropriate conditional connective as we will see in the  section on relevant logics.)