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: For all y, y will read a book if and only if y will take a plane. For all y, if y reads a book, then y is a carpenter. There is at least one y for which if y were a carpenter, then y is reading a book. For all y, y is not a carpenter.
For all y, y will not read a book can be inferred via the universal modus tollens rule. There is at least one y for which y is a carpenter if and only if y will read a book can be inferred via the existential biconditional introduction rule. There is at least one y for which y will read a book if and only if y is a carpenter can be inferred via the existential biconditional introduction rule. For all y, if y reads a book, then y is taking a plane can be inferred via the universal biconditional elimination rule. For all y, if y takes a plane, then y is reading a book can be inferred via the universal biconditional elimination rule.