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Regrets or judgements

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Use should have + a verb in past participle

to express regrets or judgments.​

I should have studied medicine

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​She shouldn't have divorced Sam

Possibility

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Use may have or might have or could have + a verb in past participle to express possibility​

I may (or might or could) have failed the final exam

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​He may (or might or could) not have been able to make a living as a painter

Ability

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Use could have + a verb in past participle to express ability.

He was the driver. He could have prevented the accident

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​The museum was closed, but he couldn't have known that. It's usually open on Tuesdays

​Certainty

​Use would have + a verb in past participle to express certainty.

You should have gone to Rio. You would have loved it

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It's good he broke up with Anne. They wouldn't have been happy together

​Conclusions

Use must have + a verb in past participle to draw conclusions

Beth isn't here. She must have gone home early.

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They didn't buy the house. The price mustn't have been acceptable