Use induction and elimination rules of propositional logic to prove

Question

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?

Answer 1

No

Where does (4) come from? And you haven't discharged your assumptions (2) and (5).

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