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 it rains, then Sarah is curious. Sarah is not curious. If James sleeps, then Joseph is sad. Sarah is curious if and only if James is sleeping. If Joseph were sad, then it is raining.
It is not raining can be inferred via the modus tollens rule. If James sleeps, then it is raining can be inferred via the transitivity rule. If Joseph were sad, then Sarah is curious can be inferred via the transitivity rule. If Sarah were curious, then James is sleeping can be inferred via the biconditional elimination rule. If James sleeps, then Sarah is curious can be inferred via the biconditional elimination rule. James is not sleeping can be inferred via the biconditional elimination rule.