Question

for any two non empty sets A and B of universal srt U. state the power of De'Morgan's law.​

Answer 1

In propositional logic and Boolean algebra, De Morgan's laws[1][2][3] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation.

De Morgan's laws represented with Venn diagrams. In each case, the resultant set is the set of all points in any shade of blue.

The rules can be expressed in English as:

• the negation of a disjunction is the conjunction of the negations
• the negation of a conjunction is the disjunction of the negations

or

• the complement of the union of two sets is the same as the intersection of their complements
• the complement of the intersection of two sets is the same as the union of their complements

or

not (A or B) = (not A) and (not B)

not (A and B) = (not A) or (not B),

where "X or Y" is an "inclusive or" meaning at least one of X or Y rather than an "exclusive or" that means exactly one of X or Y.

Answer 2

Answer:

De Morgan's Law states that 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 mentioned after the great mathematician De Morgan. This law can be expressed as ( A ∪ B) ' = A ' ∩ B '.

Step-by-step explanation:

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