CLASS-11
COMPLEMENT OF SET - LAWS OF COMPLEMENT OF SET

Laws of the Complement of a Set –

Law 1. (A’) = A, i.e., the complement of the complement of a set is the set itself.

Law 2.  ξ’ = φ  and φ’ = ξ , i.e., the complement of the universal set is the empty set and vice-versa.

Law 3.  (i)  A ∪ A’ = ξ , and  (ii)  A ∩ A’ = φ

Law 4.  De Morgan’s laws –

(a) (A ∪ B)’ = A’ ∩ B’

(b) (A ∩ B)’ = A’ ∪ B’

The following Venn diagram shows (A ∪ B)’ and (A ∩ B)’

                       (A ∪ B)’                              (A’ ∩ B’)

                            (A ∪ B)’ =  (A’ ∩ B’)

                     (A ∩ B)’                              (A’ ∪ B’)

                           (A ∩ B)’ =  (A’ ∪ B’)

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