# Complement of Sets

Complement of a set *A*, denoted by *A ^{c}*, is the set of all elements that belongs to universal set but does not belong to set

*A.*In mathematical form, complement of a set can be expressed as:

A^{c}= { x: x∈U and x∉A } In simple terms, A^{c}= U-A

Here, the complement of set *A* is computed with respect to universal set (considering set *A *is a subset of universal set *U*). This type of complement is known as **absolute complement**.

## Complement of Set Examples

### Example #1: Complement of a set with Venn Diagram

**If U = {1, 2, 3, 4, 5, 6} and A = {2, 3, 4}, find A ^{c.}**

Here, U = {1, 2, 3, 4, 5, 6} A = {2, 3, 4} ∴ A^{c}= U-A = {1, 5, 6}

### Example #2

**If U = { x:x is an integer} and A = { x:x is an even integer} then, find A ^{c}.**

Here, U = { x:x is an integer} A = { x:x is an even integer} Now, A^{c }= U - A = { x:x is an integer} - { x:x is an even integer} ∴ A^{c}= {x:x is an odd integer}

### Example #3: Complement of Union of Set

**If U = {a, b, c, d, e, f, g, h} and A∪B = {a, e, g, h}, find (A∪B) ^{c}**

^{.}

Here, U = {a, b, c, d, e, f, g, h} A∪B = {a, e, g, h}(A∪B)^{c }= U - (A∪B) ∴ (A∪B)^{c}= {b, c, d, f}