I am not understanding how to solve substitution instances, could someone please explain how it works?
- Which of the following propositional formulas are substitution instances of the formula P → (Q → P)?
If a formula is indeed a substitution instance, give the formulas substituted for P,Q.
(i) ¬R → (R → ¬R)
(ii) ¬R → (¬R → ¬R)
(iii) ¬R → (¬R → R)
(iv) (P ∧ Q → P) → ((Q → P) → (P ∧ Q → P))
(v) ((P → P) → P) → ((P → (P → (P → P))))?
(i) is a substitution instance of $P \rightarrow (Q \rightarrow P)$ because we can obtain (i) by substituting $\neg R$ for $P$ and $R$ for $Q$.
Likewise, (ii) is a substitution instance of $P \rightarrow (Q \rightarrow P)$, by substituting $\neg R$ for both $P$ and $Q$.
(iii) is, however, not a substitution instance of $P \rightarrow (Q \rightarrow P)$.
Can you do the rest from here?