Final answer:
It is false that the CIO did not believe in the 'one big union' approach; in fact, they championed the organization of large industrial unions, leading to successful worker negotiations and a merger with the AFL to form the AFL-CIO.
Step-by-step explanation:
It is false that the 'one big union' approach to union membership was not believed by the Congress of Industrial Organizations (CIO). The CIO did indeed believe in organizing large industrial unions, representing primarily unskilled and semiskilled laborers, which differed from the craft union approach of the American Federation of Labor (AFL). Under the leadership of John L. Lewis, the CIO was active in organizing large-scale industrial actions and advocating for the rights of a broad range of workers, leading to successful negotiations with large companies like General Motors and U.S. Steel. The efforts of the CIO eventually resulted in a merger with the AFL in 1955, forming the AFL-CIO.