Brake system for a motor vehicle and two methods for operating the brake system

A brake system for a motor vehicle having hydraulically actuatable wheel brakes. Each wheel an electrically actuatable inlet valve and electrically actuatable outlet valve for setting wheel-specific brake pressures. A first electrically controllable pressure provision device is connected to a brake supply line to which the wheel brakes are connected. A second electrically controllable pressure provision device is connected to the brake supply line. A first electrical device activates the first pressure provision device. A second electrical device activates the second pressure provision device. Electrically independent first and second electrical partitions are provided. The first pressure provision device and the first electrical device are assigned to the first electrical partition and the second pressure provision device, the second electrical device and the inlet and outlet valves are assigned to the second electrical partition. The inlet and outlet valves are activated by the second electrical device.