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: William is rich if and only if it is cloudy. It is raining. It is not cloudy. William is rich if and only if Jessica is writing a letter.
It is raining and it is not cloudy can be inferred via the conjunction rule. It is not cloudy and it is raining can be inferred via the conjunction rule. If William were rich, then it is cloudy can be inferred via the biconditional elimination rule. If William were rich, then Jessica is writing a letter can be inferred via the biconditional elimination rule. If it is cloudy, then William is rich can be inferred via the biconditional elimination rule. If Jessica writes a letter, then William is rich can be inferred via the biconditional elimination rule. William is not rich can be inferred via the biconditional elimination rule.