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Lecture 13

# MAT309H1 Lecture Notes - Lecture 13: If And Only If

Department
Mathematics
Course Code
MAT309H1
Professor
K.Tyros
Lecture
13

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- 
- 
- 
- T is substitutable for in :
o Q1: 
o Q2: 
- RULES OF INFERENCE <Γ, θ >
o PC
If is tautology, <Γ, θ > must be rule of inference
If Γ =ϕ, then we need θp to be a tautology
o QR: is not free in ψ, and let ϕ be a formula


PROPOSITION:    is PC
PROOF:  This is

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PROPOSITION: 
PROPOSITION:


PROOF: 




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 


We need to check that  is a tautology 
table
KNOW TILL HERE FOR QUIZ
LEMMA: 
PROOF: If then 



PC
P is a tautology


PC 
QR: 

PC