- #1
vlad dracul
- 1
- 0
hi i just need a simple yet uncomplicated proof for
(A UNION B)'S COMPLIMENTARY=A' INTERSECTION B'
(A UNION B)'S COMPLIMENTARY=A' INTERSECTION B'
De Morgan's set laws are a set of mathematical principles that explain the relationship between logical statements and their negations. They were developed by British mathematician Augustus De Morgan in the 19th century.
The two laws in De Morgan's set laws are the Law of Complement and the Law of Union. The Law of Complement states that the complement of a union of sets is equal to the intersection of their complements. The Law of Union states that the complement of an intersection of sets is equal to the union of their complements.
De Morgan's set laws are used in formal logic and in applications such as computer programming and database design. They allow for the simplification of complex logical expressions and can be used to prove the equivalence of different logical statements.
Suppose we have two sets, A and B, with elements {1, 2, 3} and {2, 4, 6} respectively. Using De Morgan's set laws, we can simplify the expression "the complement of (A union B)" to "the complement of A intersect the complement of B". This can be written as "(A' intersect B')", which is equal to the set {1, 5}.
Yes, De Morgan's set laws are applicable to all sets and can be used in any situation where logical statements are involved. They are considered to be fundamental principles in the study of set theory and logic.