Prove that A,B |- A = B where = is the triple bar?

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The discussion centers on proving the logical equivalence A, B |- A ≡ B, where "≡" denotes the triple bar. The conclusion drawn is that if both A and B are true, they share the same truth value, which can be demonstrated using logical conjunction (A & B) and disjunction (A & B ∨ ~A & ~B). This aligns with the formal definition of equivalence in propositional logic.

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  • Understanding of propositional logic
  • Familiarity with logical operators: conjunction and disjunction
  • Knowledge of logical equivalence and its definitions
  • Basic skills in formal proof techniques
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  • Study formal proofs in propositional logic
  • Learn about logical equivalence and its applications
  • Explore the use of truth tables for logical expressions
  • Investigate the role of conjunction and disjunction in logical reasoning
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powp
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Hello

is it possible to prove that

A,B |- A = B where = is the triple bar?

How do you connect the two??

Thanks

P
 
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If I read that correctly, its trivial: it just says the A, B both true implies that A and B have the same truth value!
 
You can prove it logically by conjunction (A & B) and then addition (A & B or ~A & ~B) which is the definition of equivalence.
 

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