Mr. Nance,

I was doing the exercises for Intermediate Logic Lesson 6 and got stumped by #2. In the part of the proposition that is ~q ⊃ ~p, when I was doing the defining truth table for the variables, I assumed the first variable, though out of order alphabetically, would get the TTFF pattern. But in the answer key, the letter that comes first in the alphabet (p), though the consequent, got the TTFF pattern. Why is that?

In order for a given truth table to make sense, or to compare two truth tables, the same propositions must have the same pattern of true and false. The p in the first proposition, p ⊃ q, was given TTFF, so we had to give it the same pattern for the second proposition (so we could compare apples to apples).

This could be seen, though not explicitly, in Lesson 5, in the truth table for q ⊃ p. Were one to do in this truth table what you were tempted to do in Exercise 6 #2, the p ⊃ q and the q ⊃ p would have identical patterns of true and false. But this would have been wrong, since they are not equivalent propositions.

Blessings!