Consider the following premises. For all x, x will work or x will not cook. For all x, if x works, then x is playing tennis. For all x, if x plays tennis, then x is cooking. Can we infer the following from them? For all x, x will work if and only if x will cook.
 From the fact that for all x, x will work or x will not cook we can infer that for all x, if x cooks, then x is working. From the fact that for all x, if x works, then x is playing tennis, and that for all x, if x plays tennis, then x is cooking we can infer that for all x, if x works, then x is cooking. Finally, from the fact that for all x, if x works, then x is cooking, and that for all x, if x cooks, then x is working we can infer that for all x, x will work if and only if x will cook. Therefore, the answer is yes.