I'm trying to figure out this formal proof. This is what I have so far but I'm stuck in trying to reach the goal. I'm not sure if what I did is correct so far since I'm still trying to learn this on my own. If what I provided below is confusing, I also have a screenshot of what it looks like on the Fitch program http://imgur.com/a/29m47 Thank you so much!

Premise 1. Dodec(b) v Cube(b)

Premise 2. Small(b) v Medium(b)

Premise 3. ¬Small(b) ^ ¬Cube(b)

  1. (start subproof) Small(b) ∨ Medium(b)
    1. (sub-subproof) ¬Small(b)
    2. Small(b)
    3. ⊥ (⊥ Intro 5,6)
    4. Medium(b) (⊥ Elim 7) (end subproof)

9 (start subproof) Dodec(b) v Cube(b)

  1. (start sub-subproof) ¬Small(b) ∧ ¬Cube(b)
  2. ¬Cube(b) (^ Elim10)

  3. Dodec(b) (Ana Con 9,11)

Goal: Medium(b) ∧ Dodec(b)

  • $\begingroup$ It looks like you are trying to establish $$\{D \lor C,~ S \lor M,~ \lnot S \land \lnot C\} \vdash M \land D$$ ... is that right? $\endgroup$ – DanielV Nov 12 '16 at 1:54
  • $\begingroup$ Yes, I believe so. I'm not really good at formal proofs. But I'm stuck at what do do after step 12. $\endgroup$ – ashley Nov 12 '16 at 1:55
  • $\begingroup$ Break the problem into smaller steps. First try to establish $$\{S \lor M,~ \lnot S \land \lnot C\} \vdash M$$ you'll need to use And Elimination on the second assumption, and create 2 new subproofs, one subproof will start with the premise "S" and one subproof will start with the premise "M", both of them should conclude with "M". $\endgroup$ – DanielV Nov 12 '16 at 2:00
  • $\begingroup$ Having established Medium(b) (step 8) and Dodec (b) (step 12), independently of each other and using only the premises, haven't you already reached the goal? $\endgroup$ – shardulc Nov 12 '16 at 2:53
  • $\begingroup$ You haven't established those things. You've only established them in the context of the subproofs, you want to establish them outside of the context of the subproofs. Try doing what I suggested. $\endgroup$ – DanielV Nov 12 '16 at 3:43

Thank you @DanielV for your help! I really appreciate it :) Solution


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