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Hi teachers,

A: What are you doing?
B: I am writing a letter to my father.

A:a) Why are you writing a letter to your father?

Could you tell me if we could say any of these things to mean what "A" has just asked above, please?
A.b) What are you writing a letter to your father for?
A.c) For what are you writing a letter to your father?
A.d) What is the reason of / for your writing a letter to your father?

Thank you.
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#b is possible; #c is not.
#d (with 'for') is possible, but rather formal.
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As fivejedjon says, A.d is acceptable with 'for', but I would be much more likely to phrase the question this way: What is the reason you're writing a letter to your father?
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Comments  
Mr. fivejedjon, and Mr. ozzourti, I am thankful to you for your replies!

I also heard somebody saying just "what for?". Is it possible to say just "what for", please?

For e.g.
A (to B): He boss is angry with you today.

B (B to A): What for?

Thanks again!
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LaboriousA (to B): He boss is angry with you today.B (B to A): What for?
What for? is common in everyday speech in contexts like this.