Is this usage of “know to be” correct — “They want to eat food they know to be good for them”?

Question

In the following sentence, is the construction know + to + infinitive grammatical?

They want to eat food they know to be good for them.

The dictionary says that "know to do something" is a correct construction. But can it be used in the above example?

If correct, is the meaning of the sentence similar/identical to "They want to eat food they know is good for them"? If not, what's the difference? If yes, how do they sound to a native speaker? To me as a non-native speaker, the "...know is good..." one sounds OK, but the "...know to be good..." one is sort of clumsy.

Answer 1

They want to eat food they know to be good for them is grammatical and it means the same as They want to eat food they know is good for them. Most native speakers would have no difficulty in understanding either and neither sounds particularly odd, but the first is possibly slightly more formal.

Answer 2

Either sentence is ok. The point will be made with either choice. Personally, I prefer the first one. Both sentences could be improved by adding "which" between the clauses.

They want to eat food which they know to be good for them.

or

They want to eat food which they know is good for them.

Again, both will communicate the same idea.