Symbolize each of the following.  Use the following code for the individual ideas.  Keep in mind that these can be separate sentences or just parts of a sentence, and also remember that we disregard time or sequence in our expressions.
          H: The students are happy.
          P:  Alice is prepared.
          S:  Alice is studying
          T:  There is a test on Friday.
         
1.  There is a test on Friday, but Alice is studying.

T & S

2.  Unless Alice studies she will not be prepared, but she is studying.

(S v ~P) & S

3.  The students are happy because there is not going to be a test on Friday.

H & ~T

4.  There is a test on Friday, but Alice is not prepared although she did study.

T & (~P & S)

5.  It is the case either that there is no test on Friday and the students are happy or there is a test on Friday and the students are unhappy.

(~T & H) v (T & ~H)

6.  It is not the case that Alice is studying because there is a test on Friday.

~(S & T)     For this sentence note that in a "translation" we do lose the sense of an explanation so that what we are denying is just that both things are happening together.  If that is not the intention of the speaker (she could be allowing for the possibility that both things are true but means simply to deny that the fact of the test is the explanation for Alice studying), we would have something that does not fit into the framework of what we can work with in symbolic logic. Note that if we did not have negation here there would not be the same problem (see what we have for the third statement above), even though we still lose the idea of one thing being the explanation for another.