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.

Disjoint of Sets using Venn Diagram

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, 7 is the common element of A and B.

Two sets A and B are said to be disjoint, if A ∩ B = ϕ. If A ∩ B ≠ ϕ, then A and B are said to be intersecting or overlapping sets.


Examples to show disjoint of sets using Venn diagram:

1.

Disjoint Sets using Venn Diagram

If A = {1, 2, 3, 4, 5, 6}, B = {7, 9, 11, 13, 15} and C = {6, 8, 10, 12, 14} then A and B are disjoint sets since they have no element in common while A and C are intersecting sets since 6 is the common element in both.


2. (i) Let M = Set of students of class VII

And N = Set of students of class VIII

Disjoint Sets

Since no student can be common to both the classes; therefore set M and set N are disjoint.


(ii) X = {p, q, r, s} and Y = {1, 2, 3, 4, 5}

Disjoint of Sets

Clearly, set X and set Y have no element common to both; therefore set X and set Y are disjoint sets.


3.

Disjoint of Sets Example

A = {a, b, c, d} and B = {Sunday, Monday, Tuesday, Thursday} are disjoint because they have no element in common.


4.

Two Disjoint Sets

P = {1, 3, 5, 7, 11, 13} and Q = {January, February, March} are disjoint because they have no element in common.


Note:

1. Intersection of two disjoint sets is always the empty set.

2. In each Venn diagram ∪ is the universal set and A, B and C are the sub-sets of ∪.

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 Different Situations

Relationship in Sets using Venn Diagram

Union of Sets using Venn Diagram

Intersection of Sets using Venn Diagram

Disjoint of Sets using Venn Diagram

Difference of Sets using Venn Diagram

Examples on Venn Diagram







8th Grade Math Practice

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