Consider the following premises. For all x, if x cooks, then x is writing a letter. For all x, x is a sailor or x will not write a letter. There is at least one x for which if x were a sailor, then x is cooking. Can we infer the following from them? For all x, if is not true that x will write a letter if and only if x is a sailor.
 From the fact that for all x, x is a sailor or x will not write a letter we can infer that for all x, if x writes a letter, then x is a sailor. From the fact that there is at least one x for which if x were a sailor, then x is cooking, and that for all x, if x cooks, then x is writing a letter we can infer that there is at least one x for which if x were a sailor, then x is writing a letter. Finally, from the fact that for all x, if x writes a letter, then x is a sailor, and that there is at least one x for which if x were a sailor, then x is writing a letter we can infer that there is at least one x for which x will write a letter if and only if x is a sailor, which contradicts that For all x, if is not true that x will write a letter if and only if x is a sailor. Therefore, the answer is no.