Final answer:
The statement is false. Samuel Gompers and the AFL were known for a conservative approach, focusing on negotiation to improve conditions for skilled laborers, rather than seeking revolutionary changes.
Step-by-step explanation:
The statement that the AFL under Gompers' leadership believed the existing social system should be dramatically changed by any means possible, including revolutionary methods if necessary, is false. Samuel Gompers and the American Federation of Labor (AFL) were known for their conservative approach towards labor activism. Gompers preferred negotiation over strikes and aimed to achieve better wages, shorter work weeks, and improved working conditions for skilled laborers. He was wary of more radical approaches, as was evident with movements like the Industrial Workers of the World (IWW) and the Knights of Labor, which leaned more towards radical changes in the social order through collective ownership of factories and broad inclusive memberships.