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MAT309H1 (1)
K.Tyros (1)
Lecture 13

# MAT309 Lecture 13.pdf

5 Pages
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Department
Mathematics
Course
MAT309H1
Professor
K.Tyros
Semester
Fall

Description
- - - - T is substitutable forin : o Q1: o Q2: - RULES OF INFERENCE o PC  If is tautology, must be rule of inference  If Γ =ϕ, then we need p to be a tautology o QR: is not free in ψ, and let ϕ be a formula   PROPOSITION: is PC PROOF:  This is 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 PROPOSITION: PROPOSITION: PROOF: A B C 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 ∴ tautology We need to check that is a tautologmake a truth table KNOW TILL HERE FOR QUIZ LEMMA: PROOF: If then Pick a variable y not occurring in θ Deduction of θ from PC θP is a tautology or PC Q
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