Boolean Algebra Proofs
Worksheet

Using the Boolean algebra identities, it is possible to prove that two logic circuits are equivalent. This page demonstrates how a proof should be done and then provides a few others for you to attempt.

Example Proof

This is a proof that A(A + B) is equivalent to A.

A(A + B)	=	Distributive Property AA + AB
	=	Law of Tautology: A + AB
	=	Factor (Distributive Property) A(1 + B)
	=	Law of Union: A(1)
	=	Law of Intersection: A Q.E.D.

Proof Problems

Using Boolean algebra, prove that each of the following Boolean equations is indeed true. Then draw the logic circuit for the Boolean expression on each side of the equation. Finally, create the truth table for each to verify your work.

[Hint: You can multiply any term by something equal to 1, e.g. (A + 1).]