• Implication:
  F &rarr G = ¬ F &or G
  F &harr G = (F &rarr G) &and (G &rarr F)
  
• De Morgan's Laws:
  ¬ (F &or G) = ¬ F &and ¬ G
  ¬ (F &and G) = ¬ F &or ¬ G
  
• Distributive:
  F &or (G &and H) = (F &or G) &and (F &or H)
  F &and (G &or H) = (F &and G) &or (F &and H)

Inference Rules

• Modus Ponens: P, P &rarr QQ

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