Choose the correct sentences.
a. Shall we have some coffee?
b. Please, you may post this letter for me?
c. You may take off your hat, I can't see the screen.

The correct answer is Option A (a only).

Key Points:
• Concept: Correct usage of Modals in Politeness and Request Structures.
• Explanation:
• Sentence 'a' ('Shall we have some coffee?') is a standard, grammatically correct suggestion.
• Sentence 'b' is grammatically incorrect; 'you may...?' cannot form a polite question request (would require 'Could you please post...?').
• Sentence 'c' misuses 'may' to demand action instead of granting permission ('Could you please take off...?' or 'Would you mind...').
• Official Key: Option 1 ('a only') is the official correct answer.
• Key Takeaway: Remember: 'Shall we...?' is the correct modal structure for making a polite suggestion.