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Does armor apply for explosion damage? It doesn't say you cannot so I'm guessing it does.

The normal when you write rules is that you write the rule and that rules applies unless specified otherwise. So with that in mind, armor applies to explosion damage.

The normal when you write rules is that you write the rule and that rules applies unless specified otherwise.

Of the general Hazards, both the sections on Falling and Fire specifically mention Armor applying. It also applies to the xeno's special Acid Splash. The section on Explosions is the odd one out in not having this mention, which by omission can appear intentional, though not as deliberate as stating "armor does NOT provide protection."
As it stands, most explosive weapons give a rather good chance of survivability even on a direct hit, when the target has a bit of health and armor. This has given grenades a rather weak rap in the community. From a game design perspective, of course, the devs probably don't want a 60$ piece of kit completely obliterate a common xeno in one hit, but the result is nevertheless quite lacklustre.

With the introduction of CMOM and its armor piercing explosive weapons (e.g. M111 Anti-vehicle mine, Armat Type 4 Assault Breaching Charge), it would appear any ambiguousness around armor and explosives got snuffed retroactively: there'd be no point for AP if armor was already being ignored. Hopefully this detail will nevertheless also be remedied in future versions of the Core Rule Book and Starter Set.