LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

OPERATION ON SETS - INTERSECTION OF SETS

**OPERATION ON SETS -**

**(2) Intersection of Sets –**

**The intersection of two sets A
& B is a set that contains elements that are both in A & B. The
symbol A ∩ B = {x ǀ x ∈ A, x ∈ B}**

**For Example –**

**(i) If A = {1, 2, 3, 4, 5, 6, 7,
8} and B = {2, 4, 6, 8, 10, 12, 14, 16}**

**Then, A ∩ B = {2, 4, 6, 8}**

**We can observe that, A ∩ B
⊆ A
and A ∩ B ⊆ B**

**(ii) If A = {1, 3, 5, 7}, and B = {2, 4, 6, 8}, then
these two sets do not have any common members. They are disjoint set . Their
intersection is the null set, that is, A ∩ B = ϕ**

**Two sets A & B are said to be disjoint or
mutually exclusive if and only if there is no element common to A & B,
i.e., if their intersection is the empty set, i.e., A ∩ B = ϕ**

**(iii) Let, A = {2, 4, 6, 8, 9, 10, 12}**

** B = {1, 6, 7, 10, 11, 12}**

** C = {2, 5, 8,
12, 15} then**

**A ∩ B = {2, 4, 6, 8, 9, 10, 12} ∩ {1, 6, 7, 10, 11, 12} = {6, 10, 12}**

**B ∩ A = {1, 6, 7,
10, 11, 12} ∩ {2, 4, 6, 8, 9, 10, 12} = {6, 10, 12}**

**So, A ∩ B = B ∩ A**

**Now, (A ∩ B) ∩ C = {6, 10, 12} ∩ {2, 5, 8, 12, 15} = {12}**

**Again, B ∩ C = {1, 6, 7, 10, 11, 12} ∩ {2, 5, 8,
12, 15} = {12}**

** A ∩ (B ∩ C) = {2, 4,
6, 8, 9, 10, 12} ∩ {12} = {12}**

**So, (A ∩ B) ∩ C = A ∩ (B ∩ C)**

**(iv) Let, A = {x ǀ 2x +9 = 0, x ∈ N}, B = {1, 2, 3, 4}**

**2x + 9 = 0, gives x = - 9/2 which is not a
natural number**

**So, A = ϕ**

**Or, A ∩ B = ϕ ∩ {1, 2, 3, 4} = ϕ**

**Properties Of Intersection Of Sets,**

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