Ok, so if both sentences are correct what's the difference

He will work on Tuesday or He is working on Tuesday.

For example It's Monday and I want to ask somebody whether he/ she works tomorrow, what should i say:

Are you working tomorrow ( I believe it's correct because it refers to arrangements)

Will you work tomorrow?

Is it true that if we don't know how many hours we will work or with whom we should say I will work tomorrow or ask who will I work tomorrow with

or for example it's Tuesday we have just come and want to ask our supervisor, who are we working today with or who will we work today with?
He will work on Tuesday = A future fact based on present knowledge.

He is working on Tuesday = An arrangement for the near future

For example It's Monday and I want to ask somebody whether he/ she works tomorrow, what should i say:

Are you working tomorrow ( I believe it's correct because it refers to arrangements-- Yes.)

Will you work tomorrow?-- A little odd, since it does not state a fact, but possible.

Also: Are you going to work tomorrow? Do you work tomorrow?

Is it true that if we don't know how many hours we will work or with whom we should say I will work tomorrow or ask who will I work tomorrow with-- No, not true at all.

or for example it's Tuesday we have just come and want to ask our supervisor, who are we working with today or who will we work with today?-- Both of these are OK, too, or the other options I gave above.

Do you work tomorrow?
I didn't know it is possible to use Present Simple in that way(I'm surprised)...

Is it possible to use Present Simple to express future in questions only, or it would be also correct to write:

I work tomorrow.
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I work tomorrow is also fine, as is I don't work tomorrow, so we can see a movie together.
Present simple can express scheduled future actions.

Ex. The movie starts at 10.

Ex. Tomorrow is sunday.

Ex. I have English class tomorrow.

Regards.
What do Į want to know if Į ask " will you work tomorrow? " The pure fact ir desire?
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lime grape 242fact or desire?

The two are not mutually exclusive. The 'desire' part is a fact concerning the desire of the person you are speaking to. And I would say that that's something like the fact you want to know, but it's more like willingness than desire.

Will you work tomorrow? ~ Are you willing to work tomorrow?

In any case, it takes a rather unusual scenario to make the question make sense at all. It's usually less a question of willingness than ability for people who have a job to go to tomorrow. "Will you work tomorrow?" sounds almost as if you're trying to extract a promise from someone.

Please watch these videos if you are having trouble with the various ways of expressing the future in English.

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