T4.2: 4 of 9

Sentence Structure and Punctuation

Another good rule of thumb for English sentence structure is punctuation. Consider:

If Tom and Sue are in school, then either they need a loan or very good jobs.

The comma is a key here. It sets this sentence into two parts and so marks the main connective. As a first approximation, then, write the hybrid:

(T and S) > (L or G)

Then it's obvious that the symbolization should go like this

(T&S)>(LvG)

The comma marks the main break in the sentence so commonly is a good indication of a main connective. Exceptions occur for very complex sentences including commas and a semicolon (';'). For these, the semicolon often marks the main connective.

Word Order

We have already seen example of symbolization being very sensitive to word order. This is a fairly easy point but worth emphasizing. Consider:

(7) Tom and Sue aren't both in school.

and compare it with

(8) Tom and Sue are both not in school.

The difference is obvious, if you are think carefully about it! (7) indicates that at most one of the two is in school. (8) says more, that neither is in school. So we symbolize them respectively as:

For (7):     ~(T&S)

and

For (8):     ~T&~S

How do you tell? In (7), the wording is "not both": negation first so negating the conjunction. Thus: '~(T&S)'.

On the other hand, (8) has a different word order. "Both" comes first. So it says that both of two negations are true. Thus, ampersand is the main connective: '~T&~S'.

Now you try one.

Which of the following are correct? (Use the interpretation of this page.)

  1. "Tom is in school only if Sue is in school, and they have very good jobs" can be symbolized by 'T>(S&G)'.
  2. "Tom is in school only if Sue is in school, and they have very good jobs" Can be symbolized by '(T>S)&G'.
  3. "If either Tom or Sue is not a student, then they need a loan" may be symbolized by '(~Tv~S)>L'.
  4. "If either Tom or Sue is not a student, then they need a loan" may be symbolized by '~(TvS)>L'.