Boolean Theorems and Methods of Proof

These flashcards cover key concepts and definitions related to Boolean theorems and methods of proof, essential for understanding computer engineering topics.

Commutativity

The property that B • C = C • B, which shows that the order of the variables does not affect the result.

Associativity

The property that (B • C) • D = B • (C • D), indicating that the way in which variables are grouped does not change the outcome.

Distributivity

The property that B • (C + D) = (B • C) + (B • D), demonstrating how multiplication distributes over addition.

Covering

The theorem stating that B • (B + C) = B, meaning that B combined with anything results in B.

Combining

The theorem that (B • C) + (B • C) = B; it simplifies combined terms down to a single expression.

Consensus

The theorem stating that (B • C) + (B • D) + (C • D) = (B • C) + (B • D), consolidating multiple products.

Perfect Induction

A method of proving that every input combination results in the same output for the expressions being compared.

Axioms and Theorems

Fundamental principles that help in simplifying equations, foundational to logical proofs in Boolean algebra.

Null Element

In Boolean algebra, the element that when used in an operation (like AND) yields the other operand unchanged.

Identity

A principle suggesting that operations do not change a variable when combined with a corresponding identity element.