President Theodore Roosewer's foreign policy served to increase US involvement in - China's Boxer Rebellion
Hawai's pineapple industry
latin american affairs
European alliance systems

Correct answer is Latin American affairs .

Explanation:

First option is not correct as Roosevelt was not yet president when the Rebellion was raging.

Second option is also not correct as United States didn't had many interest in Hawaii at that time.

Third option is correct as Roosevelt foreign policy was best seen in his Corollary, where he stressed out that he won't allow European forces to interfere in the situation in Latin America.

Last option is not correct as they stayed out of this alliances even when WW1 started. That is the famous policy of isolationism.

the roman empire began to fall