Which law states that the NOT operator applied to AND of two variables equals the NOT applied to each with an OR in between?

DeMorgan's Law is a fundamental principle in Boolean algebra that provides a method for transforming logical statements. Specifically, it states that the negation of a conjunction (AND operation) of two variables can be expressed as the disjunction (OR operation) of the negations of the individual variables. Mathematically, this is represented as:

¬(A AND B) = ¬A OR ¬B

This law is vital for simplifying complex logical expressions and is applied frequently in digital circuit design, programming, and various fields where logic is used.

In contrast, the other laws mentioned serve different purposes within Boolean algebra. Boolean Algebra is the overarching framework that governs all operations and relationships of logical operations. The Distributive Law concerns how operations distribute over one another, while the Identity Law defines the identity elements for AND and OR operations, which are 1 and 0 respectively. These other concepts do not specifically describe the relationship between the NOT operator and the AND operation, making DeMorgan's Law the correct choice in this context.