Originally Posted by

**lamentofking** Am I over-thinking the problem

Yes. In a truth table, variable names (i.e., names of columns) are usually listed in the alphabetical order, but this is not a law. In a formula, variables can occur in an arbitrary order. Formulas are just given to you, and you are not supposed to change them just to construct a truth table. There is nothing wrong in having a truth table with two columns p and q and the third column listing the truth values of the formula (q →¬p) ↔ (p ↔ q). This is just like having the following table listing values of an arithmetic expression.

Code:

x y | y * x
1 2 | 2
3 5 | 15
4 2 | 8
3 3 | 9

Here there is no need to switch the x and y columns even though the first variable in (y * x) is y.

You could also make the q column first. It would still be a valid truth table, but the order of truth values in the third column would be different, which may make it more difficult for your instructor to check your work.