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  • Introduction
  • Propositional logic
    • Conjunction
    • Disjunction
    • Negation
  • Predicate logic
    • Quantifiers
    • Equality
  • Theories
    • Peano arithmetic
    • Edukera

Negation

Exercises

Video examples

  • Base case: A, B, C, D; A , ~A |- B
  • With disjunction: A, B, C, D; A , ~A || C |- C
  • Variant: A, B, C, D; ~A , A || C |- C

Double Negations

  • Easy: A, B, C, D; A |- ~~A
  • More tricky: A, B, C, D; |- ~~(A||~A)
  • Implication: A, B ; ~~(A->B), ~ ~A |- ~ ~ B
  • Implication 2: A, B ; ~~A->~~B |- ~~(A->B)

De Morgan

  • First: A, B, C, D; ~A||~B |- ~(A&&B)
  • Second: A, B, C, D; ~A&&~B |- ~(A||B)
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