Each of the following arguments in English may be similarly translated, and for each, a formal proof of validity (using only the nine elementary valid argument forms as rules of inference) may be constructed. These proofs vary in length, some requiring a sequence of thirteen statements (including the premises) to complete the formal proofs. The suggested abbreviations should be used for the sake of clarity. Bear in mind that, as one proceeds to produce a formal proof of an argument presented in a natural language, it is of the utmost importance that the translation into symbolic notation of the statements appearing discursively in the argument be perfectly accurate ; if it is not, one will be working with an argument that is different from the original one, and in that case any proof devised will be useless, being not applicable to the original argument.

If Adriana joins, then the club’s social prestige will rise; and if Boris joins, then the club’s financial position will be more secure. Either Adriana or Boris will join. If the club’s social prestige rises, then Boris will join; and if the club’s financial position becomes more secure, then Wilson will join. Therefore either Boris or Wilson will join. ( A —Adriana joins; S —The club’s social prestige rises; B —Boris joins; F —The club’s financial position is more secure; W —Wilson joins.)