Final answer:
The assertion is correct; at the poles, stars circle around the zenith without rising or setting, whereas at the equator, stars rise from the east and set in the west, moving perpendicularly to the horizon.
Step-by-step explanation:
The statement is True. For an observer at the pole, stars will circle around the pole without setting. For an observer at the equator, stars rise from the east and set in the west. When at the North Pole, the celestial sphere appears to rotate around the observer with stars moving in circular paths, centered on the pole, which here coincides with the zenith. This is because the observer's horizon cuts the celestial sphere in half, and everything rotates around the zenith, where the north celestial pole is located.
None of the stars rise or set; they perpetually circle the sky. Conversely, at the equatorial region, the celestial equator bisects the sky overhead, so stars seem to rise perpendicularly from the eastern horizon and set perpendicularly on the western horizon. This is due to the fact that the celestial poles are at the horizon at the equator, with the sky’s rotation causing stars to move straight up and down from the observer's perspective.