proof - Logic deduction with Fitch system -


i working through logic , found difficulty can't solve,

how can proof premise p=>q, ¬q=>¬p?

thank you

using fitch system:

  1. p=>q............premise
  2. .| ¬q............assumption
  3. .|.| p............assumption
  4. .|.| q............implication elimination: 1,3
  5. .|.| ¬q............reiteration: 2
  6. .| p=>¬q............implication introduction: 5
  7. .| ¬p............negation introduction: 1,6
  8. ¬q=>¬p............implication introduction: 7

not neat layout, each 'indentation' represents sub-proofs done of assumptions.


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