Consider the following premises. Robert is an office clerk if and only if Patricia is a writer. For all x_12, x_12 is happy if and only if x_12 is a writer. If Robert were an office clerk, then Karen is not cooking. Karen is cooking. Can we infer the following from them? Patricia is happy.
 From the fact that for all x_12, x_12 is happy if and only if x_12 is a writer we can infer that Patricia is happy if and only if Patricia is a writer. From the fact that if Robert were an office clerk, then Karen is not cooking, and that Karen is cooking we can infer that Robert is not an office clerk. From the fact that Robert is an office clerk if and only if Patricia is a writer, and that Robert is not an office clerk we can infer that Patricia is not a writer. Finally, from the fact that Patricia is happy if and only if Patricia is a writer, and that Patricia is not a writer we can infer that Patricia is not happy, which contradicts that Patricia is happy. Therefore, the answer is no.