Texas A&M University (TAMU) PHIL 240 Introduction to Logic Exam 1 Practice

Replacement rules work by substituting a subformula with an equivalent one inside a larger formula. Because equivalence is symmetric, you can replace A with B or B with A anywhere in the formula. That bidirectional flexibility is what the directional nature is getting at: you’re allowed to move in either direction as long as the replacement is an equivalent form.

For example, if you have a subformula P ∨ Q and you know it’s equivalent to Q ∨ P, you can swap them. Or with De Morgan’s laws, ¬(P ∧ Q) is equivalent to ¬P ∨ ¬Q, so you can replace one with the other in either direction.

It’s true that replacement uses only existing formulas and does not require introducing new variables, and while replacing with an equivalent formula preserves the overall truth value of the whole expression, the essential point highlighted by the question is that the substitution can go in either direction.