The spinning system that inserts a false twist is used in both ring spinning and air-jet spinning.
1. Ring spinning: In this system, false twist is inserted into the yarn as part of the spinning process. The fibers are twisted by the rotating spindle, and the false twist helps in the formation of a well-structured yarn.
2. Air-jet spinning: In air-jet spinning, air currents are used to insert the twist into the yarn. This system also generates a false twist as it utilizes air to manipulate and twist the fibers into yarn.
Thus, both (A) Ring spinning and (C) Air-jet spinning insert false twist, making both options correct.