Consider the following premises. There is at least one x for which x is curious if and only if x will cook. For all x, x is curious or x will not cook. Can we infer the following from them? There is at least one x for which x will cook if and only if x is curious.
 From the fact that there is at least one x for which x is curious if and only if x will cook we can infer that there is at least one x for which if x were curious, then x is cooking. From the fact that for all x, x is curious or x will not cook we can infer that for all x, if x cooks, then x is curious. Finally, from the fact that for all x, if x cooks, then x is curious, and that there is at least one x for which if x were curious, 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 curious. Therefore, the answer is yes.