Let's evaluate the statements about the Brazil Current and the Gulf Stream:
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They travel in different hemispheres: This is true. The Brazil Current is located in the Southern Hemisphere, while the Gulf Stream is in the Northern Hemisphere.
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They occur in different oceans: This is also true. The Brazil Current is part of the South Atlantic Ocean, while the Gulf Stream is part of the North Atlantic Ocean.
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One begins at the equator and another one begins near the South Pole: This statement is partially true. The Brazil Current originates from the warm waters near the equator, while the Gulf Stream originates farther north but does not start near the South Pole; it flows from the Gulf of Mexico.
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One carries warm water and another carries cold water: This statement is not accurate. Both the Brazil Current and the Gulf Stream carry warm water. The Brazil Current transports warm water southward along the Brazilian coast, and the Gulf Stream carries warm water northward from the Gulf of Mexico along the eastern coast of the United States.
So, the correct statements would be that they travel in different hemispheres and occur in different oceans, but the statements regarding their origins and temperature characteristics need clarification.