Lesson 43 - Exercise 3 - I think so. / I don't think so.
Carl works. hard.
So does Harold.
In the second case ("I don't think so. "), "so" with the verb think means "No, it is not probable".
So is also used in a very similar way at the beginning of short sentences of agreement indicating "me too", or "Susan, too".
Example 1 - Past of "be":
Madelaine: I was good in school.
Susan: So was I.
Example 2 - Past of other verbs:
Madelaine: I went to Harvard University.
Susan: So did I.
Example 3 - Present Simple:
Madelaine:I always study hard.
Susan: So do I.
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