**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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