Need help solving this Existence Algorithm for truth

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SUMMARY

The discussion revolves around the Existence Algorithm involving the equation (x ¬ | ∃x) = ∅ ⊕ {∅}) ⊕ ∅. The user, Oliver, seeks clarity on whether the critical component (x ¬ | ∃x) is solvable, particularly questioning the independence of x from its reference. The conversation highlights the complexities of existential quantifiers in logic and their implications in algorithmic contexts.

PREREQUISITES
  • Understanding of existential quantifiers in logic
  • Familiarity with symbolic logic notation
  • Basic knowledge of set theory
  • Experience with algorithmic problem-solving techniques
NEXT STEPS
  • Research the principles of existential quantification in formal logic
  • Explore the implications of independence in logical expressions
  • Study set operations and their applications in algorithms
  • Learn about advanced topics in algorithmic logic, such as Gödel's incompleteness theorems
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This discussion is beneficial for mathematicians, computer scientists, and logicians who are exploring advanced concepts in algorithmic logic and existential quantifiers.

ollieha
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TL;DR
Need help solving algorithm for truth
I have an equation that I need some serious help with. I’m using a “not such that”, and I don’t know if the critical component (x ¬ | ∃x) is solvable!

Well here it is:

(x ¬ | ∃x) = ∅ ⊕ {∅}) ⊕ ∅

So if x exists independently from the reference of x, the first bit is true, but is there ever a time when that is the case?

So confused-
Oliver
 
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