Question

____i join you sir ? ( can or may )​

Answer 1

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____i join you sir ? ( can or may ).

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May I join you sir?

Answer 2

Modal Verbs show us the attitude of the speaker to what is being said or done. The term "modal" means expressing mood and mood is a way to express the attitude of the speaker.

Option C is the correct answer because it expresses possibility and it is generally used in formal sense of asking a permission with politeness applied.

Whereas option D suggests ability that was supposed to show in the past; option A suggests ability; and option B expresses certainty or assurance with which certain act is to be done in future.