So: There are
many uses of the adverb
so.
In the first case ("
I think so. "), "so" with the verb
think means "
Yes, it is probable". 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.
Now look at this. Type "So was" or "So did" or "So does":

Carl
works. hard.
So does Harold.

Ngechu
played football.
Hermann.

George Washington
was a president of the United States.
Abraham Lincoln.