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 a carpenter if and only if Elisabeth is a nurse. Elisabeth is not a nurse. If Charles reads a book, then William is a carpenter. If William were a carpenter, then Charles is reading a book.
Charles is reading a book if and only if William is a carpenter can be inferred via the biconditional introduction rule. William is a carpenter if and only if Charles is reading a book can be inferred via the biconditional introduction rule. If William were a carpenter, then Elisabeth is a nurse can be inferred via the biconditional elimination rule. If Elisabeth were a nurse, then William is a carpenter can be inferred via the biconditional elimination rule. William is not a carpenter can be inferred via the biconditional elimination rule.