Consider the following premises. There is at least one x_7 for which x_7 is a politician or x_7 is a musician. For all x_7, x_7 is not a politician or x_7 will climb a mountain. For all x_7, x_7 will cook if and only if x_7 will climb a mountain. For all x_7, if x_7 were a musician, then x_7 is cooking. Can we infer the following from them? There is at least one x_7 for which x_7 will cook.
 From the fact that for all x_7, x_7 will cook if and only if x_7 will climb a mountain we can infer that for all x_7, if x_7 climbs a mountain, then x_7 is cooking. From the fact that there is at least one x_7 for which x_7 is a politician or x_7 is a musician, and that for all x_7, x_7 is not a politician or x_7 will climb a mountain we can infer that there is at least one x_7 for which x_7 is a musician or x_7 will climb a mountain. Finally, from the fact that for all x_7, if x_7 were a musician, then x_7 is cooking, that for all x_7, if x_7 climbs a mountain, then x_7 is cooking, and that there is at least one x_7 for which x_7 is a musician or x_7 will climb a mountain we can infer that there is at least one x_7 for which x_7 will cook. Therefore, the answer is yes.