"He knows and we do not know."

Translation: Він знає, а ми не знаємо.

[yegirish]

Why is one form of 'and' accepted and the other not?

[deactivated user]

«І» doesn't work in this sentence, because «і» joins similar things, it marks joined things as belonging to roughly the same group. However, 'he knows' and 'we don't know' is not a similar thing, those sentences are contrasted, so we use «а».

[sagitta145]

It's all about the agreement between the subjects, verbs and objects of the two sentences you want to connect:

Ти любиш макарони, і ти любиш/ненавидиш рис (the subject is the same, so nothing else matters)

Ти любиш макарони, і вона любить макарони (both love; both love pasta)

Ти любиш макарони, а вона ненавидить (hate) макарони (both are about pasta, but the action is different)

Ти любиш макарони, а вона любить рис (the action is the same, but the object is different)

[ViGor72]

Він знає, та ми не знаємо. Він знає, але ми не знаємо. Без контекста ці варіанти imho цілком прийнятні, додайте будь ласка.

[sagitta145]

and -> а (in this case, and not і/й/та)

but -> але/та

So no, not in this case.