Set a and b relation result:
(1)
When A and B are disjoint sets.
A ∩ B=φ
Disjoint set mean in set theory:
Number of element in set A and number of element in set B are unequal. Then the intersection result PHY set(φ).
EXAMPLE:
A ={2,4,6}∩{1,2,3} = φ or = {}
RESULT
A ∪ B consist of all elements of A and all element of B.
Also, n(A ∪ B) = n(A)+n(B)
(2)
If A and B are overlapping, A ∩ B ≠ φ
RESULT:
A ∪ B contain all element which are
(i) in A and not in B (ii) in B and not in A
(iii) in both A and B. Also
n(A ∪ B) = n(A)+n(B) – (A ∩ B)
(3)
A ⊆ B
RESULT:
A ∪ B = B, n(A ∪ B) = n(B)
(4)
B ⊆ A, where A and B are disjoint set
RESULT:
A ∪ B = A; n(A ∪ B) = n(A)
(5)
A ∩ B = Φ
RESULT:
A ∩ B = Φ ; n(A ∩ B) = 0
(6)
A ∩ B ≠ Φ
RESULT:
A ∩ B contains all elements which are in A and B
(7)
B ⊆ A
RESULT:
A ∩ B = A ; n(A ∩ B) = n(A)
(8)
B ⊆ A
RESULT:
A ∩ B = B ; n(A ∩ B) = n(B)
Set a and b relation result
(9)
if A and B are disjoint set
RESULT:
A – B = A ; n(A – B) = n(A)
(10)
A and B are overlapping sets
RESULT:
n(A – B)= n(A) – n(A ∩ B)
(11)
A ⊆ B
RESULT:
A -B = Φ; n(A- B) = 0
(12)
B ⊆ A
RESULT:
A -B ≠ Φ; n(A -B) = n(A) – n(B)
(13)
A and B are disjoint set
RESULT:
B -A B; n(B – A) = n(B)
(14)
set A and B are overlapping set
RESULT:
n(A – B) = n(B) – n(A ∩ B)
(15)
A ⊆ B
RESULT
B – A ≠ Φ; n(B – A) = n(B) – n(A)
(16)
B ⊆ A
RESULT
B – A = Φ; n(B – A) = 0
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