-1
$\begingroup$

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?

$\endgroup$
3
  • $\begingroup$ No "induction" at all... $\endgroup$ Apr 24, 2020 at 7:39
  • $\begingroup$ You can see here as well as in many many similar posts in this site. $\endgroup$ Apr 24, 2020 at 7:41
  • 1
    $\begingroup$ The rules of inference in a natural deduction system are of introduction and elimination of the connectives (or quantifiers). $\endgroup$ Apr 25, 2020 at 2:31

1 Answer 1

2
$\begingroup$

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 ...

$\endgroup$
0

Not the answer you're looking for? Browse other questions tagged or ask your own question.