1. It is getting hotter.

2. He grew taller.
3. The leaves turned brown.
4. He fell asleep.
5. The bird came alive.
6. The man has gone blind.
7. You should stay healthy.
8. She remained unmarried all her life.
9. He became rich.
10. She appeared rich.
11. She proved rich.
12. She seemed rich.
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Are they all grammatical? Would you check all the sentences?

Yes, all are correct.

Yes, all the sentences you provided are grammatical. Here is an overview of each sentence and its grammatical structure:

1. It is getting hotter.
This sentence is grammatically correct. "It" is the subject, "is" is the linking verb, and "getting hotter" is the predicate complement describing the state of "it."

2. He grew taller.
This sentence is grammatically correct. "He" is the subject, "grew" is the past tense of the verb "grow," and "taller" is an adjective describing the state of "he."

3. The leaves turned brown.
This sentence is grammatically correct. "The leaves" is the subject, "turned" is the verb, and "brown" is an adjective describing the state of the leaves.

4. He fell asleep.
This sentence is grammatically correct. "He" is the subject, "fell" is the past tense of the verb "fall," and "asleep" is an adjective describing the state of "he."

5. The bird came alive.
This sentence is grammatically correct. "The bird" is the subject, "came" is the verb, and "alive" is an adjective describing the state of the bird.

6. The man has gone blind.
This sentence is grammatically correct. "The man" is the subject, "has gone" is the present perfect tense of the verb "go," and "blind" is an adjective describing the state of the man.

7. You should stay healthy.
This sentence is grammatically correct. "You" is the subject, "should stay" is the verb phrase, and "healthy" is an adjective describing the state of "you."

8. She remained unmarried all her life.
This sentence is grammatically correct. "She" is the subject, "remained" is the verb, and "unmarried" is an adjective describing the state of "she."

9. He became rich.
This sentence is grammatically correct. "He" is the subject, "became" is the verb, and "rich" is an adjective describing the state of "he."

10. She appeared rich.
This sentence is grammatically correct. "She" is the subject, "appeared" is the verb, and "rich" is an adjective describing the state of "she."

11. She proved rich.
This sentence is grammatically correct. "She" is the subject, "proved" is the verb, and "rich" is an adjective describing the state of "she."

12. She seemed rich.
This sentence is grammatically correct. "She" is the subject, "seemed" is the verb, and "rich" is an adjective describing the state of "she."

All the sentences use appropriate grammar and convey their intended meanings.