Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Sandbox

Comments on Prove that $A \leftrightarrow \lnot\lnot A$ (WIP)

Post

Prove that $A \leftrightarrow \lnot\lnot A$ (WIP)

+1
−0

Task

Prove that $A \leftrightarrow \lnot\lnot A$ using only the following axioms:

  1. $P \rightarrow (Q \rightarrow P)$
  2. $(P \rightarrow (Q \rightarrow R)) \rightarrow ((P \rightarrow Q) \rightarrow (P \rightarrow R))$
  3. $(P \rightarrow Q) \leftrightarrow (\lnot Q \rightarrow \lnot P)$

Scoring

Your score will be the number of times you apply any of the axioms above.

History
Why does this post require attention from curators or moderators?
You might want to add some details to your flag.

1 comment thread

Which rules of inference are allowed to be used? (2 comments)
Which rules of inference are allowed to be used?
celtschk‭ wrote almost 3 years ago

Which rules of inference are allowed to be used?

I expect modus ponens is one of them. Also, given that you don't give any axioms for $\leftrightarrow$, you'll need to allow some rules of inference for that as well.

user‭ wrote almost 3 years ago

celtschk‭ I'm really sorry, but I'm not sure what exactly rules of inference are, I've kinda given up on this draft because I don't know enough logic to make it work. Feel free to post a version of it yourself if you want, though.