# Pairs of 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

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