What State and prove De Morgan's theorem?

De Morgan's Theorem consists of two fundamental rules in Boolean algebra regarding the negation of conjunctions and disjunctions. It states that:

1. The negation of a conjunction is equivalent to the disjunction of the negations: (\neg (A \land B) = \neg A \lor \neg B).
2. The negation of a disjunction is equivalent to the conjunction of the negations: (\neg (A \lor B) = \neg A \land \neg B).

To prove these, we can use a truth table for all possible combinations of truth values for (A) and (B). By evaluating both sides of the equations for each combination, we find that the truth values match, thus confirming the validity of De Morgan's Theorem.