Imagine our Solar System is moving in the Milky Way towards a group of two stars. Star A is a Red star that is slightly closer than the Blue star (Star B). Which of these stars, if any, will give off light that is Red-shifted?

None of the stars give of light that is red-shifted

Explanation:

Motion of the observer or the source will cause a change in the wavelength of a wave. This is known as the Doppler effect. When an object and observer are getting close, blue shift occurs i. e., the wavelength gets shorter. When an object and observer are getting farther red shift occurs i. e., the wavelength gets longer.

Here, both the stars are getting closer to us so blue shift will occur.