1. I think Chuchu should live with his old master because he is a very good person. When Chuchu was almost blind, he didn't abandon Chuchu. Instead, he decided to take good care of him.

1-2. I think Chuchu should live with his old master because he is a very good person: When Chuchu was almost blind, he didn't abandon Chuchu. Instead, he decided to take good care of him.

2. I think Chuchu should live with his new master because she is warm-heated. When Chuchu was blind, she wanted to take him home with her, and has cared for him very well.

2-2. I think Chuchu should live with his new master because she is warm-heated: When Chuchu was blind, she wanted to take him home with her, and has cared for him very well.
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Would you check the sentences? How about 1-2 and 2-2? In the passages, a colon was used. Are they correct? Do we have to capitalize the word after colon?

How about 1-2 and 2-2? 1 and 1-2 sentences are both fine. 2 and 2-2 will be correct once you spell "warm-hearted" correctly and remove the commas after "her" in both sentences.

In the passages, a colon was used. Are they correct? Do we have to capitalize the word after colon?
Yes, the colons are used correctly, and yes, because you have included complete sentences after the colons, the capitalization is correct.

Thank you for yoiur help.

1. I think Chuchu should live with his old master because he is a very good person. When Chuchu was almost blind, he didn't abandon Chuchu. Instead, he decided to take good care of him.

1-2. I think Chuchu should live with his old master because he is a very good person: When Chuchu was almost blind, he didn't abandon Chuchu. Instead, he decided to take good care of him.

2. I think Chuchu should live with his new master because she is warm-hearted. When Chuchu was blind, she wanted to take him home with her and has cared for him very well.

2-2. I think Chuchu should live with his new master because she is warm-hearted: When Chuchu was blind, she wanted to take him home with her and has cared for him very well.

All correct, yes.

The sentences 1-2 and 2-2 have some minor issues. The use of a colon in both sentences is incorrect. A colon is typically used to introduce a list or to join two closely related clauses where the second clause provides further explanation or clarification of the first clause.

In sentences 1-2 and 2-2, the second part of each sentence does not provide further explanation or clarification of the first part. Instead, it provides supporting evidence for the opinion stated in the first part. Therefore, a colon is not appropriate here.

Here are the corrected versions of the sentences:

1-2. I think Chuchu should live with his old master because he is a very good person. When Chuchu was almost blind, he didn't abandon Chuchu; instead, he decided to take good care of him.

2-2. I think Chuchu should live with his new master because she is warm-hearted. When Chuchu was blind, she wanted to take him home with her and has cared for him very well.

Regarding capitalization after a colon, it depends on the style guide you are following. In general, if what follows the colon is a complete sentence, then it should be capitalized. If it is a fragment or a list, then it is not necessary to capitalize the first word after the colon.