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:
- Equivalence Style Proofs
Use Basic Equivalences to manipulate compound propositions.
Link to original - Truth Table Proofs
We can use truth tables to show that these premises are true, and therefore our conclusion is true as our proof.
Link to original - Rules of Inferences (Natural Deduction) Proofs ]])