Here we will learn about some of the laws of algebra of sets.
1. Commutative Laws:
For any two finite sets A and B;
(i) A U B = B U A
(ii) A ∩ B = B ∩ A
2. Associative Laws:
For any three finite sets A, B and C;
(i) (A U B) U C = A U (B U C)
(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)
Thus, union and intersection are associative.
3. Idempotent Laws:
For any finite set A;
(i) A U A = A
(ii) A ∩ A = A
4. Distributive Laws:
For any three finite sets A, B and C;
(i) A U (B ∩ C) = (A U B) ∩ (A U C)
(ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C)
Thus, union and intersection are distributive over intersection and union respectively.
5. De Morgan’s Laws:
For any two finite sets A and B;
(i) A – (B U C) = (A – B) ∩ (A – C)
(ii) A - (B ∩ C) = (A – B) U (A – C)
De Morgan’s Laws can also we written as:
(i) (A U B)’ = A' ∩ B'
(ii) (A ∩ B)’ = A' U B'
More laws of algebra of sets:
6. For any two finite sets A and B;
(i) A – B = A ∩ B'
(ii) B – A = B ∩ A'
(iii) A – B = A ⇔ A ∩ B = ∅
(iv) (A – B) U B = A U B
(v) (A – B) ∩ B = ∅
(vi) A ⊆ B ⇔ B' ⊆ A'
(vii) (A – B) U (B – A) = (A U B) – (A ∩ B)
7. For any three finite sets A, B and C;
(i) A – (B ∩ C) = (A – B) U (A – C)
(ii) A – (B U C) = (A – B) ∩ (A – C)
(iii) A ∩ (B - C) = (A ∩ B) - (A ∩ C)
(iv) A ∩ (B △ C) = (A ∩ B) △ (A ∩ C)
● Set Theory
● Sets
● Subset
● Practice Test on Sets and Subsets
● Problems on Operation on Sets
● Practice Test on Operations on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
● Practice Test on Venn Diagrams
8th Grade Math Practice
From Laws of Algebra of Sets to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
May 22, 24 06:21 PM
May 22, 24 06:14 PM
May 22, 24 05:17 PM
May 22, 24 03:49 PM
May 22, 24 02:33 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.