It seems to me that all the statements are true according to the article.
(a) The first sentence says, "there were no reports of casualties or destruction".
(b) Third sentence: "the quake was felt in various cities in Mindanao"
(c) Second sentence: "The undersea quake ..."
(d) First sentence says "struck the southern Phillipines", and the third sentence says "felt in ... Mindanao". Also The second sentence says that General Santos is a "southern city" and that it is on the island of Mindanao.
(e) The title says, "Quake rocks southern Phillipines".
If anything, I would have said that (c) was the most questionable as nothing says that the EPICENTER was under the sea, it just refers to it as an "undersea earthquake". Arguably the epicenter could have been on land but the force carried under the sea.
I don't know how they come up with (e) as not true. It's possible that as User170461 says, whoever wrote the answer key was thinking that the earthquake rocked only the southern Phillipines and not the whole Phillipines. But as the answer selection doesn't say "all" or "whole", I don't think that's valid. If someone said, "Maine Mendoza lives in the Phillipines", I wouldn't understand that to mean that she lives in every city and on every island of the Phillipines, just somewhere in there. Or perhaps more comparable, if I read, "There was a terrorist attack in France", I wouldn't understand that to mean that terrorists fired bullets into every square inch of France, but simply that there was a terrorist attack somewhere in that country. In any case, if that's the reasoning, than by the same reasoning (b) is false, because the article very clearly does NOT say that the quake was felt in all of Mindanao, but only in "various cities" in Mindanao.
If this was a test and the prof marked me wrong, I'd be complaining about the question.