Chapter Four, Tutorial Two
Complex Symbolizations

Here's a simple idea with which you are already familiar: The English form,

(1) If P, then Q

is symbolized as

(2)    P>Q

But this statement hides an important point about complex symbolizations. 'P' is a metavariable ranging over all sentences of SL; thus P itself may be a molecular sentence. So an instance of (1) is

(3) If Chile and Argentina are in South America, then so is Bolivia.

Which by (2) should be symbolized with main connective horseshoe (not ampersand); something like:

(4)    (C&A)>B

This may seem trivial. But the important point is that the words "If" and "then" in (1) work like the parentheses in (4). Or to put the point just a little differently, "If" and "then" in (3) serve to group Chile and Argentina together, just as parentheses do in SL. Either way, the main connective is the conditional.

The secret to doing complex symbolizations is understanding how English groups its simple sentences. We need to think about other means to group. Begin by thinking about the next question.

Which of the following are true? Click on all correct answers.

1. "Either Argentina and Bolivia are in South America, or Chile is" can be symbolized as '(A&B)vC'.
2. "Either Argentina and Bolivia are in South America, or Chile is" can be symbolized as 'A&(BvC)'.
3. "Both it's the case that either Argentina is in South America or Chile is, and Bolivia is in South America" can be symbolized as '(AvC)&B'.