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: If Charles writes a letter, then Michael is not climbing a mountain. Jessica is an astronaut or Joseph is a carpenter. Michael is climbing a mountain. Charles is writing a letter if and only if Jessica is an astronaut. It is raining.
Charles is not writing a letter can be inferred via the modus tollens rule. Michael is climbing a mountain and it is raining can be inferred via the conjunction rule. It is raining and Michael is climbing a mountain can be inferred via the conjunction rule. If Charles writes a letter, then Jessica is an astronaut can be inferred via the biconditional elimination rule. If Jessica were an astronaut, then Charles is writing a letter can be inferred via the biconditional elimination rule.