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 late. If it rains, then Robert is a carpenter. Barbara is not bored. If Robert were a carpenter, then it is raining. Robert is a carpenter if and only if Barbara is bored.
It is late and Barbara is not bored can be inferred via the conjunction rule. Barbara is not bored and it is late can be inferred via the conjunction rule. It is raining if and only if Robert is a carpenter can be inferred via the biconditional introduction rule. Robert is a carpenter if and only if it is raining can be inferred via the biconditional introduction rule. If Robert were a carpenter, then Barbara is bored can be inferred via the biconditional elimination rule. If Barbara were bored, then Robert is a carpenter can be inferred via the biconditional elimination rule. Robert is not a carpenter can be inferred via the biconditional elimination rule.