DeMorgan's law is a principle in Boolean algebra that states that the negation of a conjunction (AND) is equivalent to the disjunction (OR) of the negations of its components, and vice versa. It is named after mathematician Augustus De Morgan.
DeMorgan's law allows us to rewrite complex boolean expressions in a simpler form by distributing the negation and changing the logical operator. For example, the expression ¬(A ∧ B) can be rewritten as ¬A ∨ ¬B, making it easier to evaluate.
Yes, deMorgan's law can be applied to any boolean expression that contains logical operators (AND, OR, NOT). It is a fundamental principle in boolean algebra and can be used to simplify expressions in various contexts, such as circuit design and computer programming.
The distributive law states that the product of two expressions added to a third expression is equal to the sum of each product of the first two expressions with the third expression. DeMorgan's law, on the other hand, specifically deals with the negation of logical expressions. While they may seem similar, deMorgan's law is a more specific application of the distributive law.
Yes, deMorgan's law can be proven using logical equivalences and truth tables. It can also be derived from other fundamental laws in boolean algebra, such as the commutative and associative laws.