What are De Morgan's Laws?
Answers
Answer:
De Morgans law : 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.
These are named after the mathematician De Morgan.
The laws are as follows :
( A ∪ B)’ = A’ ∩ B’
( A∩B)’ = A’ ∪ B’
⚡Hope it will help you.⚡
Answer:
De Morgans law : 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. These are named after the mathematician De Morgan. The laws are as follows : ( A ∪ B) ' = A ' ∩ B '
where
A and B are sets,
A is the complement of A,
∩ is the intersection, and
∪ is the union.
In formal language, the rules are written as
{\displaystyle \neg (P\lor Q)\iff (\neg P)\land (\neg Q),} \neg (P\lor Q)\iff (\neg P)\land (\neg Q),
and
{\displaystyle \neg (P\land Q)\iff (\neg P)\lor (\neg Q)} \neg (P\land Q)\iff (\neg P)\lor (\neg Q)
where
P and Q are propositions,
{\displaystyle \neg } \neg is the negation logic operator (NOT),
{\displaystyle \land } \land is the conjunction logic operator (AND),
{\displaystyle \lor } \lor is the disjunction logic operator (OR),
{\displaystyle \iff } \iff is a metalogical symbol meaning "can be replaced in a logical proof with".
Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.