Let 
. Define an operation 
as 
. Check the commutative and associative properties.
Definitions:
War
Armed conflict between states, societies, or groups, characterized by the use of military force to achieve political, economic, or social objectives.
Officially Declared
A term indicating that a statement or action has been formally announced or recognized by an authoritative body or individual.
World War II
A global conflict that lasted from 1939 to 1945, involving most of the world's nations, including all of the great powers, eventually forming two opposing military alliances: the Allies and the Axis.
Foreign Policy Maker
An official or government body responsible for crafting strategies and decisions that define a nation's interactions with other countries.
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