4

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Created by
Justine Reagan

Cards (17)

  • Laws of Algebra of Sets
    • Commutative Laws
    • Associative Laws
    • Distributive Laws
    • Identity Laws
    • Inverse or Complement Laws
    • Idempotent Laws
    • Involution Law
    • De Morgan's Law
    • Absorption Laws
    • Set Difference Law
  • Commutative Lawsā€Ø
    š“ āˆŖ šµ = šµ āˆŖ š“
    š“ āˆ© šµ = šµ āˆ© š“
  • Associative Lawsā€Ø
    š“ āˆŖ (šµ āˆŖ š¶) = (š“ āˆŖ šµ) āˆŖ š¶
    š“ āˆ© (šµ āˆ© š¶) = (š“ āˆ© šµ) āˆ© š¶
  • Distributive Lawsā€Ø
    š“ āˆŖ (šµ āˆ© š¶) = (š“ āˆŖ šµ) āˆ© (š“ āˆŖ š¶)
    š“ āˆ© (šµ āˆŖ š¶) = (š“ āˆ© šµ) āˆŖ (š“ āˆ© š¶)
  • Identity Lawsā€Ø
    š“ āˆŖ Ƙ = š“
    š“ āˆ© š‘ˆ = š“
    š“ āˆŖ š‘ˆ = š‘ˆ
    š“ āˆ© Ƙ = Ƙ
  • Inverse or Complement Lawsā€Ø
    š“ āˆŖ š“š‘ = š‘ˆ
    š“ āˆ© š“š‘ = Ƙ
    š‘ˆš‘ = Ƙ
    Ƙš‘ = š‘ˆ
  • Idempotent Lawsā€Ø
    š“ āˆŖ š“ = š“
    š“ āˆ© š“ = š“
  • Involution Lawā€Ø
    (š“š‘)š‘ = š“
  • De Morgan's Lawā€Ø
    (š“ āˆŖ šµ)š‘ = š“š‘ āˆ© šµš‘
    (š“ āˆ© šµ)š‘ = š“š‘ āˆŖ šµš‘
  • Absorption Lawsā€Ø
    š“ āˆŖ (š“ āˆ© šµ) = š“
    š“ āˆ© (š“ āˆŖ šµ) = š“
  • Set Difference Lawā€Ø
    š“ - šµ = š“ āˆ© šµš‘
  • The aforementioned laws can be verified by the use of the Venn-Euler diagram
  • Idempotent Lawā€Ø
    • š“ āˆŖ š“ = š“
    š“ āˆ© š“ = š“
  • Associative Lawā€Ø
    • š“ āˆŖ (šµ āˆŖ š¶) = (š“ āˆŖ šµ) āˆŖ š¶
  • The principle of duality of sets states that when the operations of union and intersection, empty set and the universal set or any of the laws of sets are interchanged, a new valid equation is formed
  • Principle of Dualityā€Ø
    • (šµ āˆŖ š¶) āˆ© š“ = (šµ āˆ© š“) āˆŖ (š¶ āˆ© š“)
    (šµ āˆ© š¶) āˆŖ š“ = (šµ āˆŖ š“) āˆ© (š¶ āˆŖ š“)
  • Proving Set Identitiesā€Ø
    Example 1: (š“ āˆŖ šµ) āˆ© (šµ āˆŖ š¶) = (š“ āˆ© š¶) āˆŖ šµ
    Example 2: š“š‘ āˆŖ (šµ āˆŖ š¶)š‘ = (š“ āˆ© šµ)š‘ āˆ© (š“ āˆ© š¶)š‘