Proving logic propositions

I'm a little lost with this, can you guys provide full solutions?

The following propositions are tautologies, prove each one of them without truth table.

1)

This is (Where is a tautology.) Is this right? When can I apply ? Only when having all or ?

2) I dunno how to solve this one.

3) I dunno how to solve this one either.

4)

This would be How do I proceed there?

5) Help here too.

6) Another help here.

7)

We have What's next?

8) Help here again :(

9) Need help here too.

That's it, I'm lost with this, I hope you can help me. :)