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You should be patient (Bogdan)

You should try to lose weight

You should call him (Sasha)

She should tell her the truth. Dasha

You should  do your homework faster (Lia)
You'd better hurry up.

You’d beter never linger after Elena Alexandrovna’s lessons. - Yury

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May I take this cake, Bogdan?

May I open the window. Dasha

Can I come to your place right now? (Lia)

May I come in, Elena Alexandrovna? - Yury

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Would you like to try this snack? (Lia)

Would you? like to take this ice cream (Bogdan)

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Let’s go to the cinema tomorrow. (Rita)

We shoul hurry up! (Malak)
Let’s play with pup! (Sasha)

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Elena Alexandrovna, could you give us more HW? - Yury
Could you be quieter? (Lia)

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May I stay here? (Sasha)
You can stay here (Lia)
May I come with you? (Malak)

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Elena Alexandrovna could be anywhere

Elena must be at school
She might be at school

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He might leave soon (Sasha)

I might go to the school tomorrow (Malak)

Elena Alexandrovna might be anywhere. - Yury

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Elena Alexandrovna could be at the door. - Yury

We could have 5 in English (Malak)

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You must not go for a walk without cap. (Rita)

You must not leave school without Elena Alexandrovna’s permission. - Yury

You can’t smoke there. Dasha

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We don’t need to do our math homework (Malak)
We don’t need to do our HW (Sasha)

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Positive
strong obligation

Children have to go to school.

(sometimes 'have got to')

strong obligation (possibly based on the speaker's opinion)

I must study today.

mild obligation or advice

You should save some money.

Negative

no obligation

I don't have to work on Sundays.

You don't have to eat anything you don't like.

negative obligation

You mustn't smoke here.

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You can speak 4 languages (Malak)
I can hold my breath for one and half minute (Lia)

You are able to enter the canteen without Elena Alexandrovna’s permission. - Yury