Mathematical Logic

Formal logic and proof systems

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What I do

  • Apply propositional and predicate calculus
  • Construct mathematical proofs
  • Analyze logical equivalence and validity
  • Work with formal proof systems
  • Apply Boolean algebra and logic circuits
  • Study model theory and computability

When to use me

When proving theorems, designing logic circuits, or studying formal systems.

Key Concepts

  • Propositional Logic: Variables p,q,r with operators ∧,∨,¬,→,↔
  • Predicate Logic: Quantifiers ∀,∃ with predicates
  • Truth Tables: Evaluate compound propositions
  • Modus Ponens: From p and p→q, infer q
  • Proof by Contradiction: Assume ¬P, derive contradiction, conclude P
  • Boolean Algebra: Identities like De Morgan's laws ¬(p∧q) = ¬p∨¬q

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