For each of the claims of entailment shown below, construct a derivation using only the basic rules and annotate it to show explicitly how it is the result of following the procedure given in 3.5.3. Provide one note for each pass through the procedure—i.e., one note for each stage followed by one for the final pass through the procedure that confirms that the derivation is done. Each note should indicate (i) the open gap chosen (or the fact that all gaps are closed), (ii) the proximate argument of this gap and either the rule (or rules) by which it may be closed or the rule (or rules) that may be applied to develop it, and (iii) whether the gap is closed, developed, or marked as a dead end (together with the rule used if there was a choice).

More than one derivation using the basic rules can be constructed for each of the claims of entailment below. In each case construct two and also recognize any further possibilities by noting each stage at which there was a choice between different ways of developing the derivation.