Class 11 || Sets || Laws of Algebra of Sets

1. Commutative Laws

For any two finite sets A and B;

1. A U B = B U A
2. A ∩ B = B ∩ A

2. Associative Laws

For any three finite sets A, B and C;

1. (A U B) U C = A U (B U C)
2. (A ∩ B) ∩ C = A ∩ (B ∩ C)

Thus, union and intersection are associative.

3. Idempotent Laws

For any finite set A;

1. A U A = A
2. A ∩ A = A

4. Distributive Laws

For any three finite sets A, B and C;

1. A U (B ∩ C) = (A U B) ∩ (A U C)
2. 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;

1. A – (B U C) = (A – B) ∩ (A – C)
2. A - (B ∩ C) = (A – B) U (A – C)

De Morgan’s Laws can also we written as:

1. (A U B)’ = A' ∩ B'
2. (A ∩ B)’ = A' U B'

More laws of algebra of sets:

6. For any two finite sets A and B

1. A – B = A ∩ B'
2. B – A = B ∩ A'
3. A – B = A ⇔ A ∩ B = ∅
4. (A – B) U B = A U B
5. (A – B) ∩ B = ∅
6. A ⊆ B ⇔ B' ⊆ A'
7. (A – B) U (B – A) = (A U B) – (A ∩ B)

7. For any three finite sets A, B and C

1. A – (B ∩ C) = (A – B) U (A – C)
2. A – (B U C) = (A – B) ∩ (A – C)
3. A ∩ (B - C) = (A ∩ B) - (A ∩ C)
4. A ∩ (B △ C) = (A ∩ B) △ (A ∩ C)

Thank you very much for reading carefully, if you have any other questions, you can share it with us through comments, if this information was important to you, please let us knows through comments.

Please do comment and share.

Thank You.