Consider the following premises. If it snows, then it is raining. If Sarah were an office clerk, then it is raining. Sarah is not an office clerk. If it rains, then Sarah is an office clerk. It is snowing or Elisabeth is a mechanic. Can we infer the following from them? Elisabeth is not a mechanic.
 From the fact that if Sarah were an office clerk, then it is raining, and that if it rains, then Sarah is an office clerk we can infer that Sarah is an office clerk if and only if it is raining. From the fact that Sarah is an office clerk if and only if it is raining, and that Sarah is not an office clerk we can infer that it is not raining. From the fact that if it snows, then it is raining, and that it is not raining we can infer that it is not snowing. Finally, from the fact that it is snowing or Elisabeth is a mechanic, and that it is not snowing we can infer that Elisabeth is a mechanic, which contradicts that Elisabeth is not a mechanic. Therefore, the answer is no.