CMPUT272 Lecture Notes - Lecture 17: Halting Problem, Idempotence, Knuth'S Algorithm X

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November 4 2014
ETLC 2-001
Sets
Element Methods
Venn Diagrams
Algebraic Rules
Associative
(P ∩ Q) ∩ R = P ∩ (Q ∩ R)
(P Q) R = P (Q R)∪ ∪ ∪ ∪
Distributive
P ∩ (Q R) = (P ∩ Q) (P ∩ R)∪ ∪
P (Q ∩ R) = (P Q) ∩ (P R) ∪ ∪
Idempotent
P ∩ P = P
P P = P
Double Negation
P = P∼∼
DeMorgan
(P ∩ Q) = P Q ∪ ∼
(P Q) = P ∩ Q∼ ∪
Absorption
P (P ∩ Q) = P
P ∩ (P Q) = P
Commutative
P ∩ Q = Q ∩ P
P Q = Q P∪ ∪
Bound
P ∩ = ∅ ∅
P ∩ U = P
P = P∪ ∅
P U = U
Negation
P ∩ ( P) = ∼ ∅
P ( P) = U∪ ∼
Tabular Method
Example
Simplify ( ((A B) ∩ C) B)∼ ∼ ∪ ∼
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