All Questions
6
questions with no upvoted or accepted answers
2
votes
0
answers
136
views
Circular Induction
Question: Suppose you have
a circle with equal numbers of 0’s and 1’s on it’s boundary, there is
some point I can start at such that if and travel clockwise around the
boundary from that point, I will ...
user693646
1
vote
0
answers
109
views
How to Complete this Proof about wffs in Propositional Logic?
For any wff $\mathfrak{F}$, define $\mathfrak{F}^*$ as the wff derived from $\mathfrak{F}$ by replacing all $\wedge$ with $\vee$ and all $\vee$ with $\wedge$.
Claim: If all of the connectives of wff $...
- 515
1
vote
0
answers
442
views
Proof by induction, logic
I'd like you to comment if my following proof by induction is correct ($\mathbb{N} = \{0, 1, 2, \ldots\}).$
Thesis: Every formula constructed from variable $p$ and connectives $\land$, $\lor$, $\top$ ...
- 393
0
votes
1
answer
54
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Prove Every Axiom Instance Has A Property
Consider an axiom form $\phi \rightarrow \phi$. I need to show that every instance of this has an even number of $\neg$'s.
I'm not sure how to proceed.
Here is what I've tried. I've assumed some ...
- 255
0
votes
0
answers
493
views
Proof of Replaceability of Equivalent Formulas by Structural Induction
My class discussed the following theorem for which I wasn't able to make it to class. Its proof is supposed to involve structural induction but I am stuck in the inductive step...
Let B |=| C. If A' ...
- 1,180
0
votes
1
answer
104
views
How to prove the that no formula can be represented in the form (F . G),
"No formula can be represented in the form (F . G), where F and G are
formulas and is a binary connective, in more than one way.
By representing a formula in the form ¬F or (F . G) we start “parsing”...
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