Why not E?

Hi @Claudia-Frankel, Thanks for the question! So let’s take a look at what we’re being told. If Hastings’s dismissal was justified, then he was either incompetent or else disloyal. To diagram: Dismissal justified —> Incompetent v Disloyal (where “v” means “OR”) Now, we know that Hastings was never incompetent, or ~I. So then the argument concludes that Hastings must have been disloyal. Now we’re asked for an assumption upon which this argument depends. Well, right now the pieces we have are Dismissal justified —> Incompetent v Disloyal ~Incompetent Conclusion: Disloyal And what do we need here? Well, we need to know that this dismissal was justified! If this is true, it triggers the first conditional, and we know that Hastings was either incompetent or disloyal. Since he wasn’t incompetent, he must’ve been disloyal. But this is only true if the dismissal was justified in the first place, and this is what (A) tells us. Notice that if we negate (A) and say that Hastings’s dismissal wasn’t justified, we can’t conclude that Hastings was disloyal as a matter of logical necessity. (E), on the other hand, isn’t an assumption that’s required by the argument. Even if (E) were assumed, we still can’t conclude based on (E) that Hastings was disloyal, because “disloyal” is in the sufficient condition in (E). Hope this helps! Feel free to ask any other questions that you might have.