#mathematical logic

5 messages · Page 1 of 1 (latest)

next basin
#

L1 and L2 for reference:
L1: B→(C→B)
L2: (B→(C→D))→((B→C)→(B→D))

Q: Build sequences of formulas representing the following proofs(only the axiom schemas L1 and L2 and Modus Ponens are necessary)
A→(A→B)├ A→B

How Iam trying to solve this:

  1. A→(A→B) : hypothesis
  2. (A→(A→B))→((A→A)→(A→B)) : [L2]
  3. (A→A)→(A→B) : MP from 2 and 1
    Iam stuck here, don't know what to do next. (Exercise states that there should be a sequence of 9 formulas )
crisp anvilBOT
#
  1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  2. Wait patiently for a helper to come along.
  3. Once someone helps you, say thank you and close the thread with:
    +close
  4. Feel free to nominate the person for helper of the week in #helper-nominations
  5. Do not ping the mods, unless someone is breaking the rules.
  6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
next basin
#
  1. A→(A→B) hypothesis
  2. (A→(A→B))→((A→A)→(A→B)) : [L2]
  3. (A→A)→(A→B) : MP no 2. un 1.
  4. (A→((A→B)→A))→((A→(A→B))→(A→A)) : [L2] B=A, D=A, C=A→B
  5. (A→((A→B)→A)): [L1] B=A, C=A→B
  6. (A→(A→B))→(A→A): MP no 4. un 5.
  7. (A→A) : MP from 6. and 1.
  8. (A→B) : MP from 3. and 7.
#

+close