Consider the following premises. William is running if and only if James is excited. For all x_10, x_10 will not write a letter. William is running if and only if Barbara is writing a letter. Can we infer the following from them? James is excited.
 From the fact that for all x_10, x_10 will not write a letter we can infer that Barbara is not writing a letter. From the fact that William is running if and only if Barbara is writing a letter, and that Barbara is not writing a letter we can infer that William is not running. Finally, from the fact that William is running if and only if James is excited, and that William is not running we can infer that James is not excited, which contradicts that James is excited. Therefore, the answer is no.