1) Predict the likely position the United States would take if: 

2) In 1830, Great Britain sent troops to occupy Argentina (a free nation after 1816) 

3) In 1830, Spain sent troops to occupy the Spanish colonies in South America

 

Answer:

The Monroe Doctrine, came about from President James Monroe's annual message to congress in December 1982. President Monroe declared then, that the US would not be indifferent to imposition of colonial rule by the European powers on any part the American continent since it would endanger the peace and interests of the US. [1]

The Monroe Doctrine articulates that "With the existing colonies or dependencies of any European power we have not interfered, and shall not interfere. But with the governments who have declared their independence, and maintained it, and whose independence we have, on great consideration, and on just principles, acknowledged, we could not view any interposition for the purpose of oppressing them, or controlling, in any other manner, their destiny, by any European power in any other light than as the manifestation of an unfriendly disposition towards the United States."[2]

The doctrine further stated that "It is impossible that the allied powers should extend their political system to any portion of either continent, without endangering our peace and happiness: nor can any one believe that our Southern Brethren, if left to themselves, would adopt it of their own accord. It is equally impossible, therefore, that we should behold such interposition, in any form, with indifference." [2]

The above statements make it clear that if Great Britain sent troops in 1830 to occupy Argentina, a nation that was free/independent since 1816, it would force the US to intervene, perhaps by sending in its own troops. This is because Britain's act would have been viewed as an attempt to impose British rule in Argentina which would directly contravene US interests and peace in South America.

On the other hand, if Spain were to send troops in 1830, to occupy the Spanish colonies in South America, the US would not intervene, since President Monroe clearly stated that the US would not interfere in the matters of the existing European colonies in the continent.