yes, you're right

right again

they also ask me to find out whether this stament is a tautology

[(p->~q)^q]->~p

i got as answer that this is not a tautology

you were doing so well, but this is incorrect.

finally they ask me to by using morgan laws translate the following statement into a statement that means the same thing.

The exam was easy and I studied all night.

my answer is

I studied all night then the exam was easy.

recall what DeMorgan's Laws say, there are two of them (that I know of):

Law 1:

Law 2:

The statement we have is of the form

That is,

= "The exam was easy"

= "I studied all night"

So then,

= "The exam was hard" or if you want to be technical, "The exam was not easy"

= "I did not study all night"

So, the answer you are looking for is:

= "It is not true that the exam was hard or that I did not study all night"