Final answer:
The false statement is 'd) planetary nebulae usually have black holes at their centers', as stars forming planetary nebulae end their lives as white dwarfs, not black holes.
Step-by-step explanation:
The statement that is FALSE is:
d) planetary nebulae usually have black holes at their centers
Planetary nebulae are formed during the late stages of the evolution of low to intermediate-mass stars. Unlike the explosive deaths of massive stars which can result in the formation of black holes, the stars that create planetary nebulae are not massive enough to form a black hole after they shed their outer layers. These stars end their lives as white dwarfs, not black holes. Planetary nebulae can have structures such as rings or layers due to pulsations of the star before it sheds its outer layers. They tend to last for tens of thousands of years and are typically a few light-years in size, and the Sun is expected to form a planetary nebula at the end of its life.