Can & May - correct meaning

The doctor can see you at eleven.

• A. I’m not sure if she’s free at eleven.

• B. I’m suggesting a time for an appointment.

May I borrow your pen for a moment?

• A. Asking a close friend or colleague.

• B. Asking a teacher or in a formal situation.

We can have a look at the shops.

• A. I’m making a suggestion

• B. I’m describing a future ability.

May I interrupt?

• A. At a formal business meeting.

• B. At a family lunch.

You may not park here after 6 PM.

• A. It’s allowed to park here.

• B. It’s prohibited to park here after 6 PM.

I might visit my grandparents this weekend.

• A. I am not sure if I will visit them or not.

• B. I’ve definitely made plans to visit them.

You can come to the party if you want.

• A. You’re invited, but it’s optional.

• B. You are not allowed to come to the party.

We may as well stay home.

• A. There’s no better option, so staying home is fine.

• B. We absolutely must stay home.

You may not bring drinks into the auditorium during the performance.

• A. It’s up to you to decide.

• B. It’s forbidden.

You can’t possibly expect me to agree with that decision.

• • A. I absolutely refuse to agree with the decision.

• • B. I find it unlikely that I will agree, but I might.