Consider the following premises. If it rains, then Michael is a mechanic. Charles is a poet. If Charles were a poet, then it is raining. If Susan plays squash, then Michael is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: Michael is a mechanic.
 From the fact that Charles is a poet we can infer that Charles is a poet or Susan is playing squash via addition. From the fact that if Charles were a poet, then it is raining, and that if it rains, then Michael is a mechanic we can infer that if Charles were a poet, then Michael is a mechanic via transitivity. Finally, from the fact that if Charles were a poet, then Michael is a mechanic, that if Susan plays squash, then Michael is a mechanic, and that Charles is a poet or Susan is playing squash we can infer that Michael is a mechanic via disjunction elimination. Therefore, the answer is yes.