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: It is not sunny. Sarah is taking a plane if and only if William is a writer. If it is overcast, then Sarah is taking a plane. It is overcast or William is a writer. It is sunny or William is climbing a mountain.
William is climbing a mountain can be inferred via the disjunctive syllogism rule. If Sarah takes a plane, then William is a writer can be inferred via the biconditional elimination rule. If William were a writer, then Sarah is taking a plane can be inferred via the biconditional elimination rule.