Final answer:
The statement is false; the National Labor Relations Act of 1935 was enacted to protect workers' rights to unionize and prevent employer interference, not to allow companies to establish company unions.
Step-by-step explanation:
The statement that the National Labor Relations Act of 1935 allowed companies to establish company unions to assure the integrity of unions is false. The National Labor Relations Act, also known as the Wagner Act, was designed to protect the rights of workers to organize and to prevent employers from interfering with union activities. The Act also led to the creation of the National Labor Relations Board (NLRB) to arbitrate disputes between employers and unions.
During the 1930s, there was a significant rise in union membership, which correlates with a more union-friendly legal environment. Post-World War II, however, the Taft-Hartley Act of 1947 made the legal climate less encouraging for union formation by allowing states to enable workers to opt out of unions, which contributed to a decline in union membership.