Consider the following premises. For all z, if z plays a game, then z is cooking. For all z, if z takes a plane, then z is cooking. For all z, if z were sad, then z is taking a plane. There is at least one z for which z will play a game or z is sad. For all z, if z takes a plane, then z is a musician. For all z, if z were a musician, then z is sad. Can we infer the following from them? There is at least one z for which z will cook.
 From the fact that for all z, if z takes a plane, then z is a musician, and that for all z, if z were a musician, then z is sad we can infer that for all z, if z takes a plane, then z is sad. From the fact that for all z, if z were sad, then z is taking a plane, and that for all z, if z takes a plane, then z is sad we can infer that for all z, z is sad if and only if z will take a plane. From the fact that for all z, z is sad if and only if z will take a plane we can infer that for all z, if z were sad, then z is taking a plane. From the fact that for all z, if z were sad, then z is taking a plane, and that for all z, if z takes a plane, then z is cooking we can infer that for all z, if z were sad, then z is cooking. Finally, from the fact that for all z, if z plays a game, then z is cooking, that for all z, if z were sad, then z is cooking, and that there is at least one z for which z will play a game or z is sad we can infer that there is at least one z for which z will cook. Therefore, the answer is yes.