CST 329 - Week 3

This was our third week in CST 329 - Reasoning with Logic.

Chapter 6 - Conditional Derivations

Conditional Derivation or Subproof: Subproofs allow us to prove conclusions when we would otherwise not be able to do so with a inference rule. When making a subproof we assume that the initial premise is true. Once the subproof is done we cannot use it other than to show the associated conclusion.
 
Proof with a subproof for (Φ→Ψ)
 
 

Invalid proof using a subproof.

In line 7 it references line 3, leading to a invalid argument. 

 
 
Proof with a subproof using conjunctions
 

Proof with multiple subproofs
 
 Theorem: A sentence that can be proved without premises.
 
Proof for a theorem/tautology
 

Chapter 7 - "Or"

v: The symbol for "Or". So (Φ or Ψ) would be written as (Φ v Ψ). Two sentences linked by an "Or" is called a disjunction, and each sentence is a disjunct. Disjunctions are an "inclusive or". 
 
Truth Table for (Φ v Ψ)
 

Modus Tollendo Ponens

Addition




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