The
complement of the union of two sets is the intersection of their complements
and the complement of the intersection of two sets is the union of their
complements.These are called De Morgan’s laws
De
Morgan’s Laws:
For
any two sets A and B the following laws known as De Morgan’s laws, hold
1.
(A∪ B)′ = A′∩ B ′, and
Fig. 7: Augustus De
2.
(A∩ B)′ = A′∪ B′
De
Morgan’s laws can also be expressed as
1.
A ~ (B∪ C) = (A~ B) ∩ (A~
C)
2.
A ~ (B∩ C)= (A~ B) ∪ (A~ C) Fig. 7:
Augustus De
Each
of the properties above corresponds to a related property for mathematical
statements
in logic
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