During the Second Spanish Period, the following occurred:
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The Treaty of Paris (1763) gave Florida to Spain. - This is correct as Florida was ceded to Spain from Britain after the Seven Years' War.
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Significant battles of the Revolutionary War took place. - This statement is incorrect concerning the Second Spanish Period, as significant battles of the American Revolutionary War predominantly took place in other locations, rather than in Florida.
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Pinckney’s Treaty established the northern boundary of Florida. - This is somewhat accurate in the context of treaties related to Florida; however, Pinckney's Treaty (1795) mainly addressed navigation and trade on the Mississippi River and defined borders between the United States and Spanish Florida.
Lastly, regarding a large number of Patriots and Loyalists from northern states moving to Florida, this is not accurate in relation to the Second Spanish Period.
In summary, the only true statement that occurred during the Second Spanish Period is that the Treaty of Paris (1763) gave Florida to Spain.