Natural Deduction Proofs

Question

I need help with natural deduction proofs for the equation $P \to [(Q \land \neg Q) \to R]$ and I don't know how to do so. I am not even sure how to start.

Answer 1

I need help with natural deduction proofs for the equation $P \to [(Q \land \neg Q) \to R]$ and I don't know how to do so. I am not even sure how to start.

$P \to [(Q \land \neg Q) \to R]$ is a statement. Further, it is a conditional statement.

If provable as a tautology (a statement that is valued as true for all evaluations for its literal terms (ie $P,Q,R$)) then it can be proven by using a conditional proof.

A conditional proof takes the form of assuming the antecedent aiming to derive the consequent, so that the assumption may be discharged to deduce the conditional statement.

That is where you start.

The exact form this takes will depend on which of the various natural deduction system you are using, and just what rules for inference you are allowed to use.