# Pairs of Sets

If there is some relation between two sets such sets are called pairs of sets.

Pairs of sets are equal sets, equivalent sets, disjoint sets and overlapping sets.

Equal sets

Two sets are said to be equal, if they contain the same elements.

Examples:

1) A = { 1, 2, 3 } and B = { 1, 2, 3 }

As the two sets contain the same elements so set A and set B are equal sets

It is denoted as
A = B

Equivalent sets

Two sets are equivalent if and only if, a one to one correspondence exists between them

Examples

As set A and set B are equivalent sets.

It is denoted as
A ↔ B

2) A = { x | x ∈ N, x ∠ 5 } and B = { x | x is a letter word DEAR}

Solution:
A = { x | x ∈ N, x ∠ 5 }

A = { 1, 2, 3, 4 }

B = { D, E, A, R}

N(A) = n(B)

∴ A ↔ B

Disjoint sets

Two sets are disjoint, if they have no element in common.

Examples :

1) A = { 1, 2, 3} and B { 4, 5, 6}

Set A and set B are disjoint since there is no common element in them.

2) A {x|x ∈ N} and B {x | x ∠ o, x ∈ Z}

Solution:
A = {x|x ∈N}

A = { 1, 2, 3, 4 …}

B = { x|x ∠o , X ∈ Z}

B = {-1, -2, -3 … }

As there is no common element in set A and set B, So they are disjoint

Overlapping Sets

If two sets A and B have some elements in common then they are called overlapping sets

Examples:

1) A = { 2, 3, 4} and B = {3, 4, 5}

In set A and set B there are two common elements 3 and 4

Set A and set B are overlapping sets

Set Theory

Sets
Representation of Set
Cardinal Number
Types of Sets
Pairs of Sets
Subset
Complement of Set
Union of the Sets
Intersection of Sets
Operations on Sets
De Morgan's Law
Venn Diagrams
Venn-diagrams for sets
Venn-diagrams for different situations
Problems on Intersection of Two Sets
Problems on Intersection of Three Sets