MHB How to figure out the shortest path using dijkstra algorithm?

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To determine the shortest path using Dijkstra's algorithm, it's essential to understand the algorithm's mechanics and how to apply it to a graph. Users are encouraged to share their attempts and specific challenges to facilitate constructive feedback. Visual representations of work can help clarify the approach taken. Engaging with the community by demonstrating effort is crucial for receiving effective assistance. Providing a clear context and details about the problem enhances the likelihood of getting accurate guidance.
yakin
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What have you tried? What are your thoughts on the problem, are you stuck somewhere? Could you please show a minimum of effort in your questions? :confused:
 
Bacterius said:
What have you tried? What are your thoughts on the problem, are you stuck somewhere? Could you please show a minimum of effort in your questions? :confused:

Actually, i have done my work. Just wanted to know if it is correct. Here is an image of my work.View attachment 2437
 

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I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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