"These actions alone will not reduce the chances of this happening again to 0 but it will help" No it won't. There is so many already out there it will just resort to the black market or people making them on their own. You see how well making drugs illegal has helped the war on drugs right? Criminals will be criminals, all restricting them will do will cause Jim and Joe weekend shooters to not be able to take their AR15 to the woods and have some fun with beer cans.
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