Statement Forms

We have described each of the connectives in terms of a truth table. From the point of view of modern symbolic logic, compound statements involving these connectives are therefore truth-functional. That is, the truth or falsity of the compound statement is a function solely of the truth values of its components and does not depend on any other connection between the components.

So far, we have dealt with compound statements containing a single connective and two components (or just one in the case of negation). We can also put together much more complex statements, involving any number of connectives and components. To do so, however, we need some rules of punctuation to avoid ambiguities.


Comprehension Questions

1 What is the proper symbolization of "p if q?"
a) q>p
b) p>q
c) ~q>p
d) none of the above
2 What is the proper symbolization of "p only if q?"
a) p>q
b) ~q>p
c) p>q
d) none of the above
3 What is the proper symbolization of "p unless q?"
a) p>q
b) ~q>p
c) q>p
d) none of the above
4 Which of the following choices is the correct symbolization of the proposition below?

If you do not take the midterm, then either you must make it up or you fail the class. (T = you take the midterm, M = you make up the midterm, F = you fail the class)

a) T > (M v F)
b) ~T > (M v F)
c) ~T > (M . F)
d) T > (M > F)
5 Which of the following choices is the correct symbolization of the proposition below?

If I ask you one more time and you don't comply, then I will be forced to either take drastic actions or to call the authorities. (A = I ask you one more time, C = you comply, D= I will be forced to take drastic actions, H = I will be forced to call the authorities)

a) (A > ~C) v (D v H)
b) (A v ~C) > (D . H)
c) (A > ~C) > (D . H)
d) (A . ~C) > (D v H)
6 Which of the following choices is the correct symbolization of the proposition below?

Philosophy will be easy, if it is an introductory course taught by Professor Smith, but if it is an upper level course taught by Professor Smith, then it will be difficult. (I = the philosophy course is an introductory course, S = the course is taught Professor Smith, E = the course is easy, U = the philosophy course is an upper level course, D = the course is difficult)

a) (I . S . E) > (E v D)
b) [(I . S) > E] . [(U . S) > D]
c) [(I>S) . E] . [(U v S) > D]
d) [(I .S) > E] v [(U v S) > D]


Rules of punctuation

Computing Truth Values

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