# Use induction and elimination rules of propositional logic to prove [duplicate]

I was asked to prove p -> q |- ¬p or q by nature induction

1. $$p \rightarrow q$$ premise
2. p assume
3. q $$\rightarrow e,1$$
4. $$¬ p \rightarrow ¬ q$$
5. ¬p assume
6. ¬p or q or-i, 3-5

is it correct?

• No "induction" at all... Apr 24, 2020 at 7:39
• You can see here as well as in many many similar posts in this site. Apr 24, 2020 at 7:41
• The rules of inference in a natural deduction system are of introduction and elimination of the connectives (or quantifiers). Apr 25, 2020 at 2:31

Hint: use a reductio proof -- i.e. assume $$\neg(\neg p \lor q)$$ and derive a contradiction ...