LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

COMPLEMENT OF SETS

**COMPLEMENT
OF SET**

**Given the
universal set U, the complement or complementary set ) of a set A is the set of
those elements of U which are not elements of A. it is denoted by A' or A ^{c }. symbolically, A’ = { x : x ∈ U and x ∉ A }. In other words, we can say that A’ is the difference of the universal set U & A. **

** A' or A ^{c }^{ }=
U – A **

**For better understanding, we will give you some example-**

**Example.1)**

**Let, U = { 1, 2, 3, 4, 5
}, and A = { 1, 3, 5 }, then we have to
find out U – A = ?**

**Then, A’ = U – A = { 1, 2,
3, 4, 5 } - { 1, 3, 5 } = { 2, 4 }**

**Example.2) **

**Let, U = { x : x ∈ N and x ≤ 12 } and A
= { x : x ∈ W and 5 ≤ x ≤ 9 }**

**Then, U = { 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12 } and A = {
5, 6, 7, 8, 9 }**

**Thus, A’ = U – A **

** = {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } - { 5, 6, 7, 8, 9 }**

** = { 1, 2, 3, 4, 10, 11, 12 }**

** **