I've been reading Strunk and White's The Elements of Style, in which this rule is outlined:
Place a comma before and or but introducing an independent clause. Examples: The early records of the city have disappeared, and the story of its first years can no longer be reconstructed. The situation is perilous, but there is still one chance of escape.
Furthermore, on Wikipedia's page on the independent clause's subject (https://en.wikipedia.org/wiki/Subject_(grammar)), this example is given:
Zero (but implied) subject. 'Take out the trash!'
Thus, if 'Take out the trash' is an independent clause (with the implied subject being the person who the order is being directed to), would it be correct to write sentences like:
'Take out the trash, and move the bike!' 'Stop complaining, and do your homework.' 'Get off your horse, and drink your milk.'
I feel like the answer should be 'No' and that the correct way to write it is 'Take out the trash and move your bike!', however, I don't know why.