Final answer:
The statement is false as both the Homestead Strike and the Ludlow Massacre were marked by violent conflict and did not demonstrate peaceful resolution between unions and management.
Step-by-step explanation:
The statement that 'The Homestead Incident, unlike the Ludlow Massacre, showed the public that union and management officials could resolve their differences in a non-violent fashion' is false.
The Homestead Strike of 1892 was characterized by violent clashes between steelworkers and private security agents hired by Carnegie Steel. These confrontations resulted in several deaths and a legacy of violence associated with labor disputes during that era. Comparatively, the Ludlow Massacre of 1914 was ignited by the conflict between coal miners and the Colorado National Guard and resulted in further deaths, including those of miners' family members.
Both incidents were marked by severe violence and highlighted the extent to which labor disputes could escalate, reflecting poorly on the labor movement in the public eye and challenging the solidarity of workers.