Is there any rule governing the choice of aspect following forms of должен? It seems that in a negative sentence with должен, the best choice is often the imperfective, i.e.:
Мы не должны были терять очки.
Even with regards to this, though, I am not sure, since Google shows almost as many results using the perfective as the imperfective in sentences such as "Mы [не] должни были выигрывать/выиграть." (The imperfective is still more common.) So:
Which aspect is generally correct in a positive sentence with должен? Can one use both? (If so, is there truly a difference in meaning?)
Which aspect is generally correct in a negative sentence with должен? ("")
Which aspect is generally correct in a question with должен? What about a negative question, i.e. [ ]?
Не должны ли мы стремиться к такому идеалу народной жизни...