What is the proper grammar for the following sentence

Is the following sentence correct? "The patient is not like you or I." Thanks.

Is the following sentence correct? "The patient is not like you or I." Thanks.

If we take "like" as a conjunction, the sentence is :up:

Is the following sentence correct? "The patient is not like you or I."

No.
To be correct, the sentence would have to be:
"The patient is not like you or I are." - and no self-respecting native speaker would say that.
To be a conjunction - where 'you and I' is in the nominative case - the second verb needs to be present, and seem natural, as in :
"You should try to get a scholarship like I did."

As it is, 'like' is informal in most of its uses, and so then to use the grammatical formality of 'you and I' compared to 'you and me' when it is not required, is some perverse over-kill.

In your sentence, 'like' is a preposition, taking the objective case, and so should be:
"The patient is not like you or me."

"The patient is not like you or I are -- this sentence is ungrammatical and illogical

X or Y means either one of them --> singular (are?!)

No, the second verb may be ellipted.
"like" and "than" both may function as subordinating conjunctions introducing an adverbial clause.
Now read this:

Than is both a subordinating conjunction, as in She is wiser than I (am), and a preposition, as in She is wiser than me.... Since the following verb am is often dropped or “understood,” we regularly hear than I and than me. Some commentators believe that the conjunction is currently more frequent than the preposition, but both are unquestionably Standard.

also read this:
http://www.bartleby.com/68/25/825.html

"The patient is not like you or I are." - and no self-respecting native speaker would say that.

It really doesn't matter whether I had written as I did, or
"The patient is not like you or I is" - nobody would include a second verb in the sentence. It is patently obvious that 'You and/or I is' would never occur, but that "You and I are" does. I tried to give the inclusion of a verb some verisimilitude by the collocation of "I" with 'are", rather than "is"
.......... but the inclusion of a verb at all renders it a travesty, to be treated as such, not subjected to some misguided grammatical scrutiny.

Pu-LEEEEEEEEze! Try to see the broader picture.

David, you seem to be the only English speaker in the world whose words I never manage to understand.

"The patient is not like you or I are." - and no self-respecting native speaker would say that.

It really doesn't matter whether I had written as I did,

I think it does in this situation:

Is the following sentence correct? "The patient is not like you or I."

No.
To be correct, the sentence would have to be:
"The patient is not like you or I are

For that sentence to be correct, you should've written something like this:
The patient is not like you and I (=we) are.

Still better:
The patient is not like you or me.
The patient is not like (=as) you are or I am.

svartnik: David, you seem to be the only English speaker in the world whose words I never manage to understand.

You do have a dictionary, so such sweeping - and convenient - statements only attest to your practice in this forum of making some...any... attack as the response of choice when discussion requiring judgment, logic and focused thinking proves to be beyond you.

Far be it from me to comment further on your cavalier attitude (when responding to matters arising in this forum requiring a knowledgeable opinion), when you yourself blithely write:
I did not study the use of articles from books. I play them by ears.

I will comment: the idiom is 'play it by ear', just to be on the safe side for other learners in this forum.
and
It is 'study it in books' and 'learn it from books'

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