The complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A' or A\(^{C}\) or U – A or ~ A and is defined the set of all those elements of U which are not in A. Thus, A' = {x ∈ U : x ∉ A}. Clearly, x ∈ A' ⇒ x ∉ A (A – B) is also called the complement … [Read more...]

## Symmetric Difference using Venn Diagram

The symmetric difference using Venn diagram of two subsets A and B is a sub set of U, denoted by A △ B and is defined by A △ B = (A – B) ∪ (B – A) Let A and B are two sets. The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B. Thus, A △ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B} or, A △ B = {x : [x ∈ A and x ∉ B] or [x ∈ B and x ∉ … [Read more...]

## Difference of Sets using Venn Diagram

How to find the difference of sets using Venn diagram?The difference of two subsets A and B is a subset of U, denoted by A – B and is defined by A – B = {x : x ∈ A and x ∉ B}. Let A and B be two sets. The difference of A and B, written as A - B, is the set of all those elements of A which do not belongs to B.Thus A – B = {x : x ∈ A and x ∉ B} or A – B = {x ∈ A : x ∉ … [Read more...]

## Disjoint of Sets using Venn Diagram

Disjoint of sets using Venn diagram is shown by two non-overlapping closed regions and said inclusions are shown by showing one closed curve lying entirely within another. Two sets A and B are said to be disjoint, if they have no element in common. Thus, A = {1, 2, 3} and B = {5, 7, 9} are disjoint sets; but the sets C = {3, 5, 7} and D = {7, 9, 11} are not disjoint; for, … [Read more...]

## Intersection of Sets using Venn Diagram

Learn how to represent the intersection of sets using Venn diagram. The intersection set operations can be visualized from the diagrammatic representation of sets. The rectangular region represents the universal set U and the circular regions the subsets A and B. The shaded portion represents the set name below the diagram. Let A and B be the two sets. The intersection of … [Read more...]

## Union of Sets using Venn Diagram

Learn how to represent the union of sets using Venn diagram. The union set operations can be visualized from the diagrammatic representation of sets. The rectangular region represents the universal set U and the circular regions the subsets A and B. The shaded portion represents the set name below the diagram.Let A and B be the two sets. The union of A and B is the set of … [Read more...]

## Relationship in Sets using Venn Diagram

The relationship in sets using Venn diagram are discussed below: • The union of two sets can be represented by Venn diagrams by the shaded region, representing A ∪ B. A ∪ B when A ⊂ B A ∪ B when neither A ⊂ B nor B ⊂ A 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 ∩ … [Read more...]

## Venn Diagrams in Different Situations

To draw Venn diagrams in different situations are discussed below: How to represent a set using Venn diagrams in different situations?1. ξ is a universal set and A is a subset of the universal set. ξ = {1, 2, 3, 4} A = {2, 3} • Draw a rectangle which represents the universal set. • Draw a circle inside the rectangle which represents A. • Write the elements of A inside the … [Read more...]

## Venn Diagrams

Venn diagrams are useful in solving simple logical problems. Let us study about them in detail. Mathematician John Venn introduced the concept of representing the sets pictorially by means of closed geometrical figures called Venn diagrams. In Venn diagrams, the Universal Set ξ is represented by a rectangle and all other sets under consideration by circles within the … [Read more...]

## Word Problems on Sets

Word problems on sets are solved here to get the basic ideas how to use the properties of union and intersection of sets.Solved basic word problems on sets:1. Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).Solution: Using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B). then n(A ∩ B) = n(A) + n(B) - n(A ∪ B) = … [Read more...]