• The union of two sets can be represented by Venn diagrams by the shaded region, representing A ∪ B.
You are watching: 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:
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)
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> =
● 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
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