The statements about the Treaty of New Echota are as follows:
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The signers did NOT have a legal right to represent the Cherokee nation - This statement is true. The treaty was signed by a small group of Cherokee individuals (primarily Chief John Ross's political opponents) who did not have the consent of the majority of the Cherokee people, and as such, they lacked legitimate authority to represent the nation in negotiations.
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The majority of the Cherokee agreed that the treaty was fair and valid - This statement is false. The majority of the Cherokee people opposed the Treaty of New Echota and considered it unjust and invalid. The treaty was seen as a betrayal by the Cherokee Nation, leading to significant resistance and conflict.
In summary, the first statement is true, and the second statement is false.