Final answer:
The statement about the Border States quickly accepting Lincoln's proposals for gradual emancipation and willingly implementing the Thirteenth Amendment is false, as there was significant resistance and the process was neither quick nor entirely willing.
Step-by-step explanation:
The statement that the Border States quickly accepted Lincoln's proposals for gradual compensated emancipation and willingly implemented the Thirteenth Amendment is false. While President Lincoln proposed gradual emancipation as a way to end slavery without drastically affecting the economies of the Border States, these proposals were met with resistance rather than prompt acceptance.
Many of these states were hesitant to abolish slavery because they had significant populations of enslaved people and economies that were partially dependent on slave labor. The process of implementing the Thirteenth Amendment, which formally abolished slavery throughout the United States, was also neither quick nor entirely willing as it required significant political maneuvering and occurred posthumously after Lincoln's assassination.