- Thread starter
- #1

I'm trying to prove $$ : (\neg P \to \neg Q) \to (Q \to P)$$ in PL. Here's my attempt:

$ \left\{1\right\} ~~~~~~~~~~ 1. ~~~~~~ \neg P \to \neg Q ~~~~~~~~~~~~~~~~~~~~~~ \text{Premise}$

$ \left\{2\right\} ~~~~~~~~~~ 2. ~~~~~~ Q ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{Assumption for CP}$

$ \left\{1, ~ 2\right\} ~~~~~~ 3. ~~~~~~ P ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{1, 2 MT}$

$ \left\{1\right\} ~~~~~~~~~~ 4. ~~~~~~ Q \to P ~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{2, 3 CP}$

Is that correct?

$ \left\{1\right\} ~~~~~~~~~~ 1. ~~~~~~ \neg P \to \neg Q ~~~~~~~~~~~~~~~~~~~~~~ \text{Premise}$

$ \left\{2\right\} ~~~~~~~~~~ 2. ~~~~~~ Q ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{Assumption for CP}$

$ \left\{1, ~ 2\right\} ~~~~~~ 3. ~~~~~~ P ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{1, 2 MT}$

$ \left\{1\right\} ~~~~~~~~~~ 4. ~~~~~~ Q \to P ~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{2, 3 CP}$

Is that correct?

Last edited: