So I'm currently being introduced to SL and asked to prove a statement. A simple question with the premise L & W and L ⇒ ¬ F. I am asked to prove W & ¬ F. Could someone verify my solution?

So my steps are:

  1. L & W
  2. L ⇒ ¬ F
  3. W elimination
  4. L elimination
  5. ¬ F modus ponens
  6. W & ¬ F introduction


  • I’m voting to close this question because this is not a homework forum – Swami Vishwananda Nov 4 '20 at 4:11
  • You will need to edit this question and show what work you have tried. Tou ought to also include what rules were you allowed to use. The rules can differ in logic classes and textbooks. Don't think all logic is logic and it's all the same. If you are using natural deduction rules please state which ones as this can vary. Conjunction elimination is used at least twice. Conjunction intro is also used as well as modus ponens (aka conditional elimination). Show what you have tried. – Logikal Nov 4 '20 at 5:45
  • Correct......... – Mauro ALLEGRANZA Nov 4 '20 at 6:52

Yes, that is valid, although the justifications are "conjunction elimination" and "conjunction introduction". You should also include citation of line numbers.

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