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Considering he's from NJ, the statements are correct, a hunter could not possess a shotgun and a bow at the same time, as their seasons do not overlap, and it does not appear, after cursory review, that a bow could be carried during the rifle season.

There are SOME states that allow the use of archery equipment during firearms seasons (Kansas for example) such that a guy could carry a rifle as a 'back up' but do their hunting with a bow. I've carried both in the past - wanting to get a buck with my BOW, but not wanting to pass if it showed up out of my bow range.