1. I have a pen.

2. I don't have a pen.
3. I have not a pen.
4. Do you have a pen?
5. Have you a pen?
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Are they all grammatical?
Do they use #3 and #5 in The UK?

#3 is incorrect, but you could write, "I have no pen."

The others are okay.

Out of the five sentences provided, there are grammatical differences between them. Let's analyze each sentence:

1. "I have a pen." - This sentence is grammatically correct and commonly used to indicate possession of a pen.

2. "I don't have a pen." - This sentence is also grammatically correct and is the negation of sentence #1. It is commonly used to express the absence of pen possession.

3. "I have not a pen." - This sentence is less commonly used and sounds somewhat archaic or poetic. While it is technically grammatically correct, it is not commonly used in modern English. Native English speakers generally opt for "I don't have a pen" instead.

4. "Do you have a pen?" - This sentence is grammatically correct and often used to ask someone if they possess a pen. It is commonly used in both the UK and the US.

5. "Have you a pen?" - This sentence is also grammatically correct, but it sounds more formal or old-fashioned. It is more commonly used in British English and might be less common in American English.

To summarize, sentences #1, #2, #4, and #5 are grammatically correct, while sentence #3 is less commonly used in modern English. Sentences #3 and #5 are more commonly used in the UK, but the usage may vary among individuals and regions.