Question

which idea would have been in opposition to roosevelts foreign policy philosophy?
decreasing the size of the american military
sending marines into cuba
putting a blockade on venezuela
constructing the panama canal

Explanation:

Roosevelt's foreign policy (notably the Big Stick ideology) relied on a strong military to project power, intervene in Latin America (like sending marines to Cuba, blockading Venezuela), and pursue imperial infrastructure projects such as the Panama Canal. Reducing the U.S. military would directly contradict this aggressive, power-projection focused philosophy.

Answer:

decreasing the size of the American military