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

Conjunction

Exercises

Video examples

  • Commutativity: A, B; A && B |- B && A

Easy

  • Introduction: A, B; |- A -> (B -> (A && B))
  • Left elimination: A, B; |- A && B -> A
  • Right elimination: A, B; |- A && B -> B

Medium

  • Currying: A, B, C; (A && B) -> C |- A -> (B -> C)
  • Uncurrying: A, B, C; A -> (B -> C) |- (A && B) -> C
  • Weak distributivity of ∧ over ⇒: A, B, C; (A -> B) && C |- A -> (B && C)

Advanced

  • Associativity: A, B, C; |- (A && (B && C)) <-> ((A && B) && C)
  • Distributivity of ⇒ over ∧: A, B, C; |- (A -> (B && C)) <-> ((A -> B) && (A -> C))

Final boss

  • JN switch: A, B, C, D, E, F, G; (A && (B && ((C && D) -> E) -> F)) -> G |- A && D && ((B && (C -> E)) -> F) -> G
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