Final answer:
Elvin Jones and McCoy Tyner did leave the John Coltrane Quartet, but not both in 1965. Jones left in early 1966 while Tyner left in December 1965.
Step-by-step explanation:
The statement that Elvin Jones and McCoy Tyner left the John Coltrane Quartet to take on other projects in 1965 is false. Elvin Jones, the dynamic drummer, and McCoy Tyner, the innovative pianist, were essential components of the John Coltrane Quartet's classic lineup. Elvin Jones continued to play with Coltrane until late 1965. He left the band in early 1966.
McCoy Tyner parted ways with Coltrane later, in December 1965, after becoming increasingly uncomfortable with the direction in which Coltrane was taking the music, particularly as he moved into a freer, more avant-garde style with additional musicians altering the quartet's dynamic.