# 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, 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.

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

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}

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

3.

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

4.

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