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