I. Often it is necessary
to
rethink a conditional relationship in order to arrive at a standard
form of "if .... then ..." with a sufficient condition expressed as an
antecedent and a necessary condition expressed as a consequent.
Rewrite each of the following in this way, then symbolize using P and S.
1. Alice will pass if
she
studies.
If
Alice studies then she will pass. S->P
2. Bob will pass only if
he has studied.
If
Bob passes then he has studied. P->S
3. Carol will not pass
if she does not study.
If
Carol does not study then she will not pass. ~S->~P
4. Don will pass unless
he has not studied.
If
Don does not pass then he has not studied. ~P->~S
or If Don has studied then he will
pass. S->P
5. Ed has to study in
order to pass.
If
Ed passes then he has studied. P->S
6. Without study
Felicity cannot pass.
If
Felicity passes then she has studied. P->S
note that in our
paraphrase we may have to adjust the tense of a verb to reflect the
idea that one thing happens before another
7. Study is
enough for George to pass.
If
George studies then he passes. S->P
8. Harry will pass
assuming that he studies.
If
Harry studies then he will pass. S->P
II.
Symbolize each of the
following using the letters E, F, and I.
1. Logic is both easy
and interesting.
E
& I
2. Logic is not both
easy and fun.
~(E
& F)
3. If logic is either
easy or interesting it will be fun.
(E
v I) -> F
4. Logic has to be both
easy and fun in order to be interesting.
I
-> (E & F)
5. If logic is not
either easy or fun then it will not be interesting.
~(E
v F) -> ~I
6. Although logic is not
easy it will be fun if it is interesting.
~E
& (I -> F)
