Consider the following premises. For all x_5, if x_5 cooks, then x_5 is reading a book. For all x_5, if x_5 reads a book, then x_5 is a mechanic. For all x_5, x_5 will cook. There is at least one x_5 for which x_5 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Some carpenters are mechanics.
 From the fact that for all x_5, if x_5 cooks, then x_5 is reading a book, and that for all x_5, x_5 will cook we can infer that for all x_5, x_5 will read a book via universal modus ponens. From the fact that for all x_5, if x_5 reads a book, then x_5 is a mechanic, and that for all x_5, x_5 will read a book we can infer that for all x_5, x_5 is a mechanic via universal modus ponens. Finally, from the fact that there is at least one x_5 for which x_5 is a carpenter, and that for all x_5, x_5 is a mechanic we can infer that some carpenters are mechanics via existential conjunction. Therefore, the answer is yes.