In my opinion your instructor isn't doing a very good job of actually teaching you the Exposure Triangle. Apparently he/she forgot to include ISO which is 1 leg of the Exposure Triangle, Aperture and Shutter Speed being the other 2. Also, I prefer the term "opening" rather than "hole" as a descriptive term when talking about aperture.
Ignore the use of "digital" in this explanation because the Exposure Triangle applies equally to film:
http://www.digital-photography-school.com/learning-exposure-in-digital-photography
Your answers are correct as long as the ISO is held as a constant - which it is in film photography and as long as either shutter speed or aperture is also held as a constant.
Here is a hypothetical example using ISO 125 film.
Shutter Speed As a Constant:
f2 @ 1/250 sec. shutter speed = 3 stops overexposed.
f2.8 @ 1/250 sec. shutter speed = 2 stops overexposed.
f4 @ 1/250 sec. shutter speed = 1 stop overexposed.
f5.6 @ 1/250 sec. shutter speed = CORRECT EXPOSURE.
f8 @ 1/250 sec. shutter speed = 1 stop underexposed.
f11 @ 1/250 sec. shutter speed = 2 stops underexposed.
f16 @ 1/250 sec. shutter speed = 3 stops underexposed.
Aperture As a Constant
f5.6 @ 1/2000 sec. shutter speed = 3 stops underexposed.
f5.6 @ 1/1000 sec. shutter speed = 2 stops underexposed.
f5.6 @ 1/500 sec. shutter speed = 1 stop underexposed.
f5.6 @ 1/250 sec. shutter speed = CORRECT EXPOSURE
f5.6 @ 1/125 sec. shutter speed = 1 stop overexposed.
f5.6 @ 1/60 sec. shutter speed = 2 stops overexposed.
f5.6 @ 1/30 sec. shutter speed = 3 stops overexposed.
Changing Aperture and Shutter Speed to Maintain Correct Exposure
f16 @ 1/30 sec. shutter speed = CORRECT EXPOSURE.
f11 @ 1/60 sec. shutter speed = CORRECT EXPOSURE.
f8 @ 1/125 sec. shutter speed = CORRECT EXPOSURE
f5.6 @ 1/250 sec. shutter speed = CORRECT EXPOSURE.
f4 @ 1/500 sec. shutter speed = CORRECT EXPOSURE.
f2.8 @ 1/1000 sec. shutter speed = CORRECT EXPOSURE.
f2 @ 1/2000 sec. shutter speed = CORRECT EXPOSURE.