Day 36: Set Theory Laws

Hello Dear Students,
 Hope you all are doing good.

Aaj hum set theory ke laws and principles ke baare mein study karenge,

So, let's get started....

1. ABSORPTION LAW- Absorption law states that
A∪(A∩B) = A
A∩(A∪B) = A

2. ASSOCIATIVE LAW - The Association law states that
A∪(B∪C)=(A∪B)∪C
A∩(B∩C)=(A∩B)∩C

3. COMMUTATIVE LAW - The Commutative law states that
A∪B=B∪A
A∩B=B∩A

4.COMPLEMENT LAW - The complement law states that
A∩Ac
A∪Ac=U

5. COMPLEMENTATION LAW- The Complementation law states that
(Ac)c = A

6. DE-MORGAN'S LAW - The De-Morgan's law states that
(A∩B)c = Ac∪Bc
(A∪B)c = Ac∩Bc

7. DISTRIBUTIVE LAW - The Distributive law states that
A∪(B∩C) = (A∪B)∩(A∪C)
A∩(B∪C) = (A∩B)∪(A∩C)

8. DOMINANT LAW - The Dominant law states that
A∩Φ=Φ
A∪U=U

9. IDEMPOTENT LAW - The Idempotent law states that
A∪A=A
A∩A=A

10. IDENTITY LAW - Identity Law states that 
 A∪Φ = A
 A∩U = A

Other laws and principles of set are as follows-

  1. n(A∪B) = n(A)+n(B)-n(A∩B)
  2. n(A∪B) = n(A)+n(B) {For disjoint sets}
  3. n(A∪B) = n(A-B)+n(B-A)+n(A∩B)
  4. n(A) = n(A-B)+n(A∩B)
  5. n(B) = n(B-A)+n(A∩B)
  6. n(A∪B∪C) = n(A)+n(B)+n(C)+n(A∩B∩C)-n(A∩B)-n(B∩C)-n(C∩A)
  7. n((A∩B)c) = n(U)-n(A∩B)
  8. n((A∪B)c) = n(U)-n(A∪B)
  9. n(Ac∩Bc) = n(U)-n(A∪B)


INCLUSION- EXCLUSION PRINCIPLE is

  • n(A∪B) = n(A)+n(B)-n(A∩B)
  • n(A∪B∪C) = n(A)+n(B)+n(C)+n(A∩B∩C)-n(A∩B)-n(B∩C)-n(C∩A)


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    Regards,
    UGC NET EXPERTS