1. The library is open from 9 to 5.

2. The library is open 9 to 5.
3. The library is opened from 9 to 5.
4. The library is opened 9 to 5.
[Are they all grammatical?]

I think the first one would work best, and the second would be okay as well. However, the third and fourth answers don't sound quite right.

The verb "is" is present tense. The word "opened" is past tense. They don't agree. It either WAS opened from 9 to 5 at some time in the past, or it IS open from 9 to 5 on an on-going basis. Numbers one and two are both acceptable (Kathryn is right, #1 is better). Three and four are not.

Out of the four sentences you provided, only sentence 1 and sentence 2 are grammatically correct.

1. "The library is open from 9 to 5."
2. "The library is open 9 to 5."

Explanation:

Sentence 1: "The library is open from 9 to 5."
In this sentence, we use the present simple tense to indicate the regular and ongoing hours of operation for the library. The phrase "from 9 to 5" specifies the time range during which the library is open. This sentence is grammatically correct.

Sentence 2: "The library is open 9 to 5."
This sentence follows the same structure as sentence 1 but omits the word "from." However, it is still grammatically correct and conveys the same meaning: the library's hours of operation are from 9 to 5.

Sentence 3: "The library is opened from 9 to 5."
This sentence is not grammatically correct. The verb "opened" should be in the present tense to match the subject ("library") and indicate a continuous state of being.

Sentence 4: "The library is opened 9 to 5."
Similar to sentence 3, this sentence is also incorrect. The verb "opened" should be in the present tense ("open") to match the subject ("library") and convey a continuous state of being.

To summarize, only sentences 1 and 2 are grammatically correct, while sentences 3 and 4 contain errors.