MAY or CAN?

It depends on the situation...

MAY - if you ask for permission "May I leave early?"

CAN - aif you ask about ability  "Can you touch you tongue to your nose?"

I can = I am able to


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You do not say "may you"
because you would be asking that person a permission for that person...
"May you go to the beach with your friends?"
 
[ it doesn't make sense and it isn't proper English. ]
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However, "you may" can be said.
- May I go to the beach with my friends?
- You may.
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