Common Mistakes

• I think you haven’t seen my brother.✖️
• I do not think you have seen my brother.✔️
• I believe you haven’t been to Canada.✖️
• I don’t believe you have been to Canada.✔️
• Ali does not think he can live without his family.✔️

Explanation:
When "think, suppose, believe, and imagine" are used to introduce a negative clause, we most often write "not" with "think, suppose, imagine, and believe," rather than with the second verb or following clause.
Note: If we want to express surprise, we can use "not" with the second verb. In other words, we can express surprise:

• Hey! I thought you weren't (at) home.

However, the above rule isn't true for "hope." In case of "hope," we always make the second verb (which is followed by "hope") negative:

• I hope you won't divorce her for nothing.✔️
• I don't hope you divorce her for nothing.✖️

Bonus:

• How do you do? Good, thanks.✖️
• How do you do? How do you do?✔️

Reason:
Remember that "how do you do?" is not a question like "how are you?" We use "how do you do" when we get introduced to strangers or meet somebody for the first time. The usual reply is "how do you do?" Don't say "good, thanks" in reply to "how do you do?" because it is not a question.