Day 36: Set Theory Laws
Hello Dear Students,
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=Φ
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
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=Φ
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-
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)
Best of Luck Students,
A∩U = A
Other laws and principles of set are as follows-
- n(A∪B) = n(A)+n(B)-n(A∩B)
- n(A∪B) = n(A)+n(B) {For disjoint sets}
- n(A∪B) = n(A-B)+n(B-A)+n(A∩B)
- n(A) = n(A-B)+n(A∩B)
- n(B) = n(B-A)+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)
- n((A∩B)c) = n(U)-n(A∩B)
- n((A∪B)c) = n(U)-n(A∪B)
- n(Ac∩Bc) = n(U)-n(A∪B)
INCLUSION- EXCLUSION PRINCIPLE is
Best of Luck Students,
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UGC NET EXPERTS