Consider the following premises. Patricia is running if and only if Karen is playing squash. For all x, x will not write a letter. For all x, x will write a letter if and only if x will play squash. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not running or Charles is taking a plane.
 From the fact that for all x, x will write a letter if and only if x will play squash, and that for all x, x will not write a letter we can infer that for all x, x will not play squash via universal biconditional elimination. From the fact that for all x, x will not play squash we can infer that Karen is not playing squash via universal instantiation. From the fact that Patricia is running if and only if Karen is playing squash, and that Karen is not playing squash we can infer that Patricia is not running via biconditional elimination. Finally, from the fact that Patricia is not running we can infer that Patricia is not running or Charles is taking a plane via addition. Therefore, the answer is yes.