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January 26th, 2018, 03:02 AM   #1
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Joined: Jan 2018
From: Belgium

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Axioms logic problem

Hello everyone,

I am currently stuck on one problem for an assignment for a university logic course. I will provide a picture in the attachment.

I have to prove the blue formula at the bottom of the note in the picture by only using the axioms written above in pencil. I would start by using axiom 7 twice (getting rid of the universal quantifiers, so I can limit myself to axioms 2-4), and end with axiom 6 to re-introduce the universal quantifier.

The steps in-between, however, are a mystery to me, even after -literally- hours of looking for a solution. I do know that ((Ax->Rxx)->~Ax) should be equivalent to (Rxx->~Ax), so a deduction should be possible. But doing that with axioms seems to be impossible for me.

Can someone give me some more insight in these axioms or put me on the right tracks, please?

Attached Images IMG_23312.jpg (77.5 KB, 9 views) January 26th, 2018, 03:10 AM #2 Senior Member   Joined: Oct 2009 Posts: 753 Thanks: 261 Here's a solution, I'll let you formalize it in your language: Take $x$ arbitrary. Assume $A_x$. If $R_{xx}$, then $A_x\rightarrow R_{xx}$, hence by hypothesis $\neq A_x$. Contradiction. Hence $\neg R_{xx}$. Hence $A_x\rightarrow \neg R_{xx}$. Hence $R_{xx}\rightarrow \neg A_x$. So you'll want to do some proof by contradiction. The formal way of doing this is (3). Thanks from Atrend January 26th, 2018, 04:45 AM #3 Newbie   Joined: Jan 2018 From: Belgium Posts: 7 Thanks: 0 Thank you for your quick reply, Micrm@ss! Your help is greatly appreciated! Tags axioms, logic, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post John441 Applied Math 2 October 21st, 2013 01:11 PM FSU_91 Applied Math 1 May 25th, 2013 02:51 PM PlayingSolo Real Analysis 8 September 10th, 2012 11:46 AM Chiruno Real Analysis 5 August 26th, 2011 05:35 AM

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