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.
