Consider the following premises. There is at least one z_4 for which z_4 will cook if and only if z_4 will listen to a song. For all z_4, if z_4 cooks, then z_4 is listening to a song. Can we infer the following from them? There is at least one z_4 for which if z_4 listens to a song, then z_4 is cooking.
Yes.