Final answer:
The Taft-Hartley Act makes it illegal to establish a closed shop except in the construction industry by banning closed shops and union shops.
Step-by-step explanation:
The law that makes it illegal to establish a closed shop except in the construction industry is the Taft-Hartley Act. This act, passed in 1947, reversed the legislative advances made by labor unions and banned closed shops and union shops. It also prohibited secondary boycotts and required union leaders to disclaim affiliation with Communist organizations.