Final answer:
The complement of the set of people playing the piano (set P), denoted as P', includes all individuals from the set of trombone players (set T) who do not appear in set P. For the given sets, P' consists of Joe, Billy, Carol, Cesar, Juan, and Alfred.
Step-by-step explanation:
To find the complement of the set of people playing the piano (set P), denoted as P', we list all the people who are not in set P. Assuming our universal set consists of all the people mentioned in both sets P and T combined, the complement of P will include all the individuals from set T who do not play the piano.
Let's list the members of both sets:
- Set P (piano players): Alan, Tanya, Ginny, Selena, Ramon, Michelle, Sara, Jose, Hector
- Set T (trombone players): Tanya, Ginny, Joe, Sara, Billy, Carol, Jose, Cesar, Juan, Alfred
To find P', we simply list all members of set T that are not in set P:
P' (complement of P): Joe, Billy, Carol, Cesar, Juan, Alfred