We use 'Yours sincerely' or 'Sincerely urs.' at the end of a letter. Then what is the full form of 'Yours sincerely'?
1. I am your sincerely friend.
2. I am your sincerely servant.
3. I am your sincerely friend/servant.
4. I am your friend/servant sincerely.
Probably the last one is the closest. I've always taken that to mean "I am sincerely at your service." Sounds a bit weird, but then idioms usually are!
I don't think any of them is the full form.
Since "Sincerely yours" is used at the end of different kinds of letters, we don't assume that we mean either "friend" or "servant."
This site has a brief discussion of this term.
http://www.dailywritingtips.com/yours-faithfully-or-yours-sincerely/
The correct full form of "Yours sincerely" is option 3: "I am your sincerely friend/servant."
To understand this, let's break it down:
"Yours sincerely" is an example of a complimentary close, which is a polite way to end a formal letter or email. It is used to convey respect and to indicate the writer's professional or personal relationship with the recipient.
In the given options, option 1 ("I am your sincerely friend") does not make grammatical sense. It would be more appropriate to use "sincerely" as an adverb to describe the action of being a friend, such as "I sincerely am your friend."
Option 2 ("I am your sincerely servant") is grammatically correct, but it might not be the most appropriate choice of words unless the context of the letter or relationship between the writer and recipient is one of service or subservience.
Option 3 ("I am your sincerely friend/servant") combines both options 1 and 2, allowing for the possibility that the writer may possess a friendship or servant-like relationship with the recipient. This option is more flexible and can be used in various situations.
Option 4 ("I am your friend/servant sincerely") switches the order of the adverb "sincerely" and the nouns "friend" and "servant." While this option still conveys the same meaning, it breaks the common arrangement used in complimentary closes, where the adjective (friend/servant) comes before the adverb (sincerely).
Therefore, the correct and commonly used full form is option 3: "I am your sincerely friend/servant."