Complete the sentences using the modal verbs "can", "may", "must".
10. I don’t believe that they didn’t recognize you. They … (fail to recognize) you.
11. His teacher … (help) him; his English is quite decent now.
12. My students … (be) at a lecture now. They never miss classes.
13. I don’t believe it. He … (write) the letter but the signature is certainly not his.
14. … this old man (be) your brother?
15. The message … (be delivered) in time as we received an immediate answer.

10. I don’t believe that they didn’t recognize you. They may fail to recognize you.
To express doubt or disbelief about an action in the past, we can use the modal verb "may". In this case, it suggests that it is possible that they failed to recognize you.

11. His teacher must help him; his English is quite decent now.
We use the modal verb "must" to express a strong deduction or conclusion. Given that his English is quite decent now, we can strongly conclude that his teacher helps him.

12. My students must be at a lecture now. They never miss classes.
To express a strong deduction or conclusion about a present situation, we use the modal verb "must". Based on the fact that they never miss classes, we can deduce that they are currently at a lecture.

13. I don’t believe it. He may write the letter but the signature is certainly not his.
To express doubt or uncertainty about an action in the past, we can use the modal verb "may". In this case, it suggests that it is possible that he wrote the letter, but the signature certainly does not match his.

14. Can this old man be your brother?
To express possibility or uncertainty about a present situation, we use the modal verb "can". In this case, it suggests that it is possible that this old man is your brother.

15. The message must be delivered in time as we received an immediate answer.
To express a strong deduction or conclusion about a present situation, we use the modal verb "must". Given that we received an immediate answer, we can strongly conclude that the message was delivered on time.