**•** The union of two sets can be represented by Venn diagrams by the shaded region, representing A ∪ B.

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Use a venn diagram to illustrate the relationships a ⊂ b and a ⊂ c.A ∪ B when A and B are disjoint sets

• The intersection of two sets can be represented by Venn diagram, with the shaded region representing A ∩ B.

A ∩ B = ϕ No shaded part

**•** The difference of two sets can be represented by Venn diagrams, with the shaded region representing A - B.

A – B when A ⊂ B Here A – B = ϕ

Relationship between the three Sets using Venn Diagram

• If ξ represents the universal set and A, B, C are the three subsets of the universal sets. Here, all the three sets are overlapping sets. **Let us learn to represent various operations on these sets.**

A ∩ (B ∪ C)

**Some important results on number of elements in sets and their use in practical problems. Now, we shall learn the utility of set theory in practical problems. If A is a finite set, then the number of elements in A is denoted by n(A). Relationship in Sets using Venn DiagramLet A and B be two finite sets, then two cases arise: **

**Case 1: **A and B are disjoint. **Here, we observe that there is no common element in A and B. Therefore, n(A ∪ B) = n(A) + n(B)**

**Case 2:**

When A and B are not disjoint, we have from the figure **(i) n(A ∪ B) = n(A) + n(B) - n(A ∩ B) (ii) n(A ∪ B) = n(A - B) + n(B - A) + n(A ∩ B) (iii) n(A) = n(A - B) + n(A ∩ B) (iv) n(B) = n(B - A) + n(A ∩ B) **

A ∩ B

Let A, B, C be any three finite sets, then n(A ∪ B ∪ C) = n<(A ∪ B) ∪ C> = n(A ∪ B) + n(C) - n<(A ∪ B) ∩ C> = + n(C) - n <(A ∩ C) ∪ (B ∩ C)> = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C) Therefore, n(A ∪B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)

**● Set Theory**

●** ****Sets Theory**

**● ****Representation of a Set**

**● ****Types of Sets**

**● ****Finite Sets and Infinite Sets**

**● ****Power Set**

**● ****Problems on Union of Sets**

**● ****Problems on Intersection of Sets**

**● ****Difference of two Sets**

**● ****Complement of a Set**

**● ****Problems on Complement of a Set**

**● ****Problems on Operation on Sets**

**● ****Word Problems on Sets**

**● ****Venn Diagrams in DifferentSituations**

**● ****Relationship in Sets using VennDiagram**

**● ****Union of Sets using Venn Diagram**

**● ****Intersection of Sets using VennDiagram**

**● ****Disjoint of Sets using VennDiagram**

**● ****Difference of Sets using VennDiagram**

**● ****Examples on Venn Diagram**

**8th Grade Math Practice****From Relationship in Sets using Venn Diagram to HOME PAGE**

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