Laws of Algebra Upsets

Introduction

• Welcome to the channel, today's topic: Laws of Algebra of Sets
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Main Laws

1. Tempo Relief Law

• Union and Intersection with an Empty Set: You get the same set, for example, A ∪ ∅ = A and A ∩ A = A

2. Identity Law

• Union with ∅: A ∪ ∅ = A
• Intersection with Universally Set: A ∩ U = A

3. Domination Law

• Union with Universally Set: A ∪ U = U
• Intersection with ∅: A ∩ ∅ = ∅

4. Commutation Law

• Order can be changed in union and intersection: A ∪ B = B ∪ A and A ∩ B = B ∩ A

5. Associativity Law

• Associativity in union and intersection: (A ∪ B) ∪ C = A ∪ (B ∪ C) and (A ∩ B) ∩ C = A ∩ (B ∪ C)

6. Distributivity Law

• In union and intersection: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
• In intersection and union: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

7. Complementation Law

• Double complement = original set: (A')' = A

De Morgan's Laws

• First Law: (A ∪ B)' = A' ∩ B'
• Second Law: (A ∩ B)' = A' ∪ B'

Absorption Law

• Using union and intersection: A ∪ (A' ∩ B) = A ∩ (A' ∪ B) = A

Conclusion

• Use Venn diagrams when applying these laws
• Future videos will discuss quality checking and the principle of inclusion-exclusion
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