Consider the following premises. Karen is a carpenter. If Karen were a carpenter, then Elisabeth is cooking. Elisabeth is cooking if and only if Mary is a mechanic. Can we infer the following from them? Elisabeth is not cooking.
 From the fact that Karen is a carpenter we can infer that Karen is a carpenter or Mary is a mechanic. From the fact that Elisabeth is cooking if and only if Mary is a mechanic we can infer that if Mary were a mechanic, then Elisabeth is cooking. Finally, from the fact that if Karen were a carpenter, then Elisabeth is cooking, that if Mary were a mechanic, then Elisabeth is cooking, and that Karen is a carpenter or Mary is a mechanic we can infer that Elisabeth is cooking, which contradicts that Elisabeth is not cooking. Therefore, the answer is no.