# 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.

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

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

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

As set A and set B are equivalent sets.

It is denoted as

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

A = { x | x ∈ N, x ∠ 5 }

A = { 1, 2, 3, 4 }

B = { D, E, A, R}

N(A) = n(B)

∴ A ↔ B

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

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}

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

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

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

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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

• 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