Final answer:
The history of income taxation in the U.S. does not start with the Declaration of Independence; this is false. The first income tax was imposed in the 1860s to support Civil War expenses, with the 16th Amendment in 1913 formally allowing federal income tax. Jefferson did base much of the Declaration on John Locke's theories, which is true.
Step-by-step explanation:
The statement that the history of income taxation in the United States can be traced back to the Declaration of Independence is false. The first federal income tax was imposed during the 1860s, specifically to fund the Civil War efforts. The need for a consistent revenue source led to the passing of the 16th Amendment in 1913, which formally granted Congress the power to impose a federal income tax.
It is important to clarify that while the colonists' objections, as mentioned in the exercises, were not against the principle of taxation itself but rather the way the tax revenues were applied - essentially without their consent or representation - the income tax as we understand it today was not in existence at the time of the Declaration of Independence. The objection was more about 'taxation without representation'.
Regarding the Theories of John Locke and their influence on the Declaration of Independence, this is true. Thomas Jefferson drew heavily from Locke's philosophy of natural rights and the social contract when crafting the Declaration.