True or False: The TCAS processor manages traffic both 10,000 feet above and below the aircraft, even if the TAS display shows only up to 8700 feet.

The statement is true because the Traffic Collision Avoidance System (TCAS) in the T-6A is designed to monitor and manage air traffic both above and below the aircraft, providing critical information to enhance situational awareness and prevent potential collisions. Although the Traffic Advisory System (TAS) display may only show traffic up to 8,700 feet, the TCAS itself maintains an awareness of aircraft in a broader vertical range, extending up to 10,000 feet above and below the airplane's altitude. This capability is essential for ensuring safe separation from surrounding air traffic, allowing pilots to make informed decisions regarding traffic management even if the visual display is limited to a specific altitude range.

In contexts where the other answers could be considered, it's important to note that the TCAS operates independently of the display limitations, focusing on overall traffic surveillance rather than just the ranges shown on the pilot's instruments.