What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: Patricia is not a writer. If William takes a plane, then Michael is a sailor. Patricia is a writer or it is not raining. Michael is a sailor if and only if it is raining.
It is not raining can be inferred via the disjunctive syllogism rule. If it rains, then Patricia is a writer can be inferred via the rewriting rule. If Michael were a sailor, then it is raining can be inferred via the biconditional elimination rule. If it rains, then Michael is a sailor can be inferred via the biconditional elimination rule.