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Union & Intersection of Sets
1.
UNION & INTERSECTION
OF SETS MODULE 4
2.
It is the
set of elements that belongs to the two or more sets.
3.
It is formed
by getting the elements that are common to two or more sets.
4.
•Union - ∪ •Intersection
- ∩ Symbols:
5.
EXAMPLE 1 Consider the
sets 𝐴, and 𝐵: 𝐴 = 1, 2, 3, 5, 7, 9, 10 𝐵 = 1, 3, 4, 5, 6, 7, 8 A ∪ B A ∩ B = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 1, 3, 5, 7
6.
A Venn Diagram
can be used to represents the union & intersection. 𝐀 𝐁∪ 𝐀 𝐁 𝟐 𝟗 𝟏𝟎 𝟒 𝟔 𝟖 ∩ 𝐴 = 1, 2, 3, 5, 7, 9, 10 𝐵 = 1, 3, 4, 5, 6, 7, 8
7.
EXAMPLE 2 Consider the
sets 𝐴, 𝐵and 𝐶: 𝐴 = 1, 2, 5, 6, 8 𝐵 = 1, 3, 5, 7,8 𝐶 = 1, 2, 5, 7,11
8.
𝐴 = 1,
2, 5, 6, 8 𝐵 = 1, 3, 5, 7, 8 𝐶 = 1, 2, 5, 7, 11 A ∪ B A ∪ C B ∪ C A ∪ B ∪ C = 1, 2, 3, 5, 6, 7, 8 = 1, 2, 5, 6, 7, 8, 11 = 1, 2, 3, 5, 7, 8, 11 = 1, 2, 3, 5, 6, 7, 8, 11
9.
A ∩ B A
∩ C B ∩ C A ∩ B ∩ C = 1, 5, 8 = 1, 2, 5 = 1, 5, 7 = 1, 5 𝐴 = 1, 2, 5, 6, 8 𝐵 = 1, 3, 5, 7, 8 𝐶 = 1, 2, 5, 7, 11
10.
USING VENN DIAGRAM 𝐀 𝐁 𝐴
= 1, 2, 5, 6, 8 𝐵 = 1, 3, 5, 7,8 𝐶 = 1, 2, 5, 7, 11 𝐂 A ∪ B A ∪ C B ∪ C 𝐀 ∪ 𝐁 ∪ 𝐂 = 1, 2, 3, 5, 6, 7, 8 = 1, 2, 5, 6, 7, 8, 11 = 1, 2, 3, 5, 7, 8, 11 = 1, 2, 3, 5, 6, 7, 8, 11
11.
USING VENN DIAGRAM 𝐀 𝐁 𝐴
= 1, 2, 5, 6, 8 𝐵 = 1, 3, 5, 7,8 𝐶 = 1, 2, 5, 7, 11 𝐂 A ∩ B A ∩ C B ∩ C A ∩ B ∩ C = 1, 5, 8 = 1, 2, 5 = 1, 5, 7 = 1, 5
12.
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