Sets: A, B, C
Universal set: I
Complemet: A'
Empty set: ∅
Union of sets: A ∪ B
Intersection of sets: A ∩
B
Difference of sets: A ⃥ B
1. A ⊂ I
2. A ⊂ A
3. A =
B if
A ⊂ B
and B ⊂ A
4. Empty
set
∅ ⊂ A
5. Union
of sets
C = A ∪ B = {x│x ∈ A or x ∈ B}
Figure 1.
6. Commutativity
A ∪ B = B ∪ A
7. Associativity
A ∪ (B ∪ C) = (A ∪ B) ∪ C
8. Intersection of sets
C =
A ∪ B = {x│x ∈ A or x ∈ B}
Figure 2
9. Commutativit
A ∩ B = B ∩ A
10. Associativity
A ∩ (B ∩ C) = (A ∩ B) ∩ C
11. Distributivity
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
12. Idempotency
A ∩ A = A,
A ∪ A = A
13. Domination
A ∩ ∅ = ∅
A ∪ I = I
14. Identity
A ∪ ∅ = A,
A ∩ I = I
15. Complement
A' = {x ∈ I │ x ∉ A}
16. Complement
of Intersection and Union
A ∪ A' = I,
A ∩ A' = ∅
17. De Morgan’
Laws
(A ∪ B)' = A' ∩ B',
(A ∩ B)' = A' ∪ B'
18. Difference
of Sets
C = B ⃥
A = {x│x ∈ B and x ∉ A}
Figure 3
19. B ⃥ A =
B ⃥ (A ∩ B)
20. B ⃥ A =
B ∩ A'
21. A ⃥ A =
∅
22. A ⃥ B =
A if A ∩ B = ∅.
Figure 4
23. (A ⃥ B) ∩
C = (A ∩ C) ⃥ (B ∩ C)
24. A' =
I ⃥
A
25. Cartesian
Product
C = A × B = {(x, y)│x ∈ A and
y ∈ B}
Sumber
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