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 Ac . 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 Ac = 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 }