The Battle of Saratoga did not allow the British to cut off New England from the rest of the colonies.
British general John Burgoyne had proposed the plan to isolate New England from the rest of the colonies. The plan had about 8,000 British troops invading into New York from Canada and taking control of the Hudson River. The plan was initially successful -- the British took Fort Ticonderoga in June of 1777. But General Burgoyne overextended his access to supplies as he came further into Patriot territory, and the colonial forces were able to cut off his supply line. After a couple of difficult battles, Burgoyne's eventual surrender of his troops came with the loss at Saratoga in October, 1777.
I believe the answer is C) salutary neglect
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