1. have do I hope so I think so
Auxiliary Verbs,
have do
I hope so
I think so

2. Use an auxiliary verb when you want to avoid repeating some part of your sentence (because it can be deduced from the context):
Person A: Have you locked the door?
Person B: Yes, I have. (instead of "I have locked the door")
-George wasn't working, but Janet was. (instead of "Janet was working")
-She could lend me the money, but she won't. (instead of "she won't lend me the money")
Person A:Are you angry with me?
Person B: Of course I'm not. (instead of "I'm not angry")
Use "do", "does" or "did" for the present and past simple:
Person A: Do you like onions?
Person B: Yes, I do (instead of "I like onions")
Person A: Does Mark smoke?
Person B: He used to, but now he doesn't any more (instead of "He used to smoke, but now he doesn't smoke any more")

3. Have to "have + to-infinitive" is used to express duty and obligation.
We have to tidy our rooms once a week.
She had to see a doctor after 2 weeks.

4. "I think so" / "I hope so"
After certain verbs you can use "so" if you don't want to repeat something:
Person A: Are those people English?
Person B: I think so. (Meaning: "I think they are English")
Person A: Will you be at home tomorrow morning?
Person B: I expect so. (Meaning: "I expect I'll be at home.")
Person A: Do you think Kate has been invited to the party?
Person B: I suppose so. You can also say: "I hope so ", "I guess so" and "I'm afraid so" .

5. Negative Forms
I think so / I expect so I don't think so / I don't expect so
I hope so / I'm afraid so /I guess so I hope not / I'm afraid not / I guess not
I suppose so  I don't suppose so or I suppose not
"Do you think it's going to rain?" "I think so. / I don't think so.“