Final answer:
The Zhou dynasty leaders believed that losing the Mandate of Heaven, which was contingent upon just and moral governance, could occur if rulers were not fair to their people. This was indicated through warnings of natural disasters and social turmoil.
Step-by-step explanation:
Leaders of the Zhou dynasty believed in the divine justification of their rule through the Mandate of Heaven, a principle that mandated the ruler's virtue and moral governance as conditions for retaining this heavenly sanction. According to Zhou ideology, if rulers were unjust or failed in their duties by not being fair to their people, they would be warned through natural disasters and social disorder, which were seen as signs that they had lost the mandate. Consequently, the Zhou believed that they had overthrown the Shang dynasty and received the Mandate of Heaven because the Shang had become despotic and corrupt.