A proof is an argument that applies one or more

  • sound reasoning methods to a collection of
    • facts, definitions, premises to produce a conclusion that must be true whenever the premises are true

Proofs establish the validity of statements of the following form:

(premise, premise, , premise conclusion) T

  • “The conclusion follows from the set of premises”
  • “The set of premises logically implies the solution”
  • “The set of claims entails the solution”

There are multiple ways to write a proof:

  1. Equivalence Style Proofs

    Use Basic Equivalences to manipulate compound propositions.

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  2. Truth Table Proofs

    We can use truth tables to show that these premises are true, and therefore our conclusion is true as our proof.

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  3. Rules of Inferences (Natural Deduction) Proofs ![[Natural Deduction Proofs)](Proofs Using Rules of Inferences (Natural Deduction Proofs|Proofs Using Rules of Inferences (Natural Deduction Proofs)]])