# Shorter Truth Tables for Equivalence

Mr. Nance,

I have a question Lesson 11 of Intermediate Logic. I have all of the right answers to the exercises, but I noticed that on a few of the questions, I wrote more lines in my answers because I thought I had to be exhaustive in my efforts to find no contradiction. A specific example would be #5. I agree that there is only one way for the conditional to be false. But, there are multiple ways the conditional can be true. Why didn’t you try lines with I as true and C false, or C false and I true? Am I misinterpreting the fourth instruction from p.70 to “switch the assigned truth values and try again”? Is this directive leveled at each whole proposition, or at each constant? (I hope this is making sense).

The directive is leveled at the whole proposition, since you are trying to determine the equivalence of the whole propositions. You are trying to show that the whole propositions cannot have opposite truth values (for equivalence), or that the whole propositions can have opposite truth values (for non-equivalence). It seems to me that doingÂ what you are suggesting would be no different than doing a longer truth table for equivalence.

Blessings!