Complement of a Set
Complement of a set
Let U be the universal set and let A be a set such that A ⊂ U. Then the complement of A with respect to U is denoted by A’ or Ac or U-A and is defined the set of all those elements of U which are not in A.
Thus A’={ x : x ∈ U and x ∉ A}
Clearly x ∈ A’ ⇔ x∉A
In Fig (10) shaded region represents A’
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| Fig (10) |
Example
Let the set of natural numbers N={ 1, 2, 3, 4…….} be the the universal set and let A = {2, 4, 6, 8…… } then A’={1, 3, 5…..}