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