0

We have these axioms and modus ponens:

Axiom 1 is: P→(Q→P)

Axiom 2 is: (P→(Q→R))→((P→Q)→(P→R))

Axiom 3 is:(P→Q)→(¬Q→¬P)

Modus ponens is: from P and P→Q infer Q

Edit: I still couldn't solve it, so I would really appreciate it if someone gave me a hint

Using these axioms and modus penons I want to infer V from (U → V ), (¬U→V)

Using axiom 3 I said that (V→ (U → V ) ) → (¬ (U →V ) → ¬V ). And using axiom 1 I said that V→ (U → V ). So using modus ponens we can infer that ¬ (U →V ) → ¬V.

If I could somehow write ¬ (U →V ) using one of these axioms then I could infer ¬V.

I'm a bit stuck here. Any help please?

  • Welcome to SE Philosophy! Thanks for your contribution. Please take a quick moment to take the tour or find help. You can perform searches here or seek additional clarification at the meta site. Don't forget, when someone has answered your question, you can click on the checkmark to reward the contributor. – J D Nov 5 '20 at 21:25
  • I’m voting to close this question because this is not a homework forum – Swami Vishwananda Nov 6 '20 at 4:25
  • It's not homework – aneys Nov 7 '20 at 10:57

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.