Final answer:
Yes, it is true that Elia Kazan decided to cooperate with HUAC by testifying and naming names of individuals involved in the Communist Party, which has affected his legacy in the film industry.
Step-by-step explanation:
The statement that Elia Kazan was determined to cooperate with the House Committee on Un-American Activities (HUAC) is true. Kazan, a well-known film director, decided to testify before HUAC in 1952, and in his testimony, he named names of colleagues who had been involved in the Communist Party with him. This action effectively ended several careers but allowed Kazan to continue working in Hollywood. His decision to cooperate with HUAC has been a controversial part of his legacy, eliciting both criticism for his perceived betrayal and acknowledgment for his career achievements despite the difficult circumstances of the McCarthy era.