Consider the following premises. It is snowing if and only if Joseph is a cashier. It is snowing. If Joseph were a cashier, then Patricia is a writer. If Patricia were a writer, then it is snowing. Can we infer the following from them? Joseph is not a cashier.
 From the fact that if Joseph were a cashier, then Patricia is a writer, and that if Patricia were a writer, then it is snowing we can infer that if Joseph were a cashier, then it is snowing. From the fact that it is snowing if and only if Joseph is a cashier we can infer that if it snows, then Joseph is a cashier. From the fact that if Joseph were a cashier, then it is snowing, and that if it snows, then Joseph is a cashier we can infer that Joseph is a cashier if and only if it is snowing. From the fact that Joseph is a cashier if and only if it is snowing we can infer that if it snows, then Joseph is a cashier. Finally, from the fact that if it snows, then Joseph is a cashier, and that it is snowing we can infer that Joseph is a cashier, which contradicts that Joseph is not a cashier. Therefore, the answer is no.