1. How did Thomas Jefferson use John Locke's ideal of the sodal contract to justify declaring independence?

The famous introduction clearly reflected John Locke's social contract theory: "...to secure these rights [Life, Liberty, and the pursuit of happiness], Governments are instituted among Men, deriving their just powers from the consent of the governed."

There are several reasons why the Declaration of Independence (1776) was written, with some of them being:

To declare that the thirteen colonies in America were no longer under British rule, but were now sovereign states. The declaration also served a secondary purpose of ending the Revolutionary War waged against Great Britain. It declared that all men were equal and that they had the right to pursue happiness, effectively instating the values that were meant to run our future country.