SQUARE45

Let

A, B, C

be Boolean variables. The fundamental laws governing simplification include:\n1. Idempotence:

A \land A = A

and

A \lor A = A

.\n2. Complementarity:

A \land \neg A = 0

and

A \lor \neg A = 1

.\n3. Commutativity:

A \land B = B \land A

and

A \lor B = B \lor A

.\n4. Associativity:

(A \land B) \land C = A \land (B \land C)

and

(A \lor B) \lor C = A \lor (B \lor C)

.\n5. Absorption:

A \land (A \lor B) = A

and

A \lor (A \land B) = A

.\n6. Distributivity:

A \land (B \lor C) = (A \land B) \lor (A \land C)

and

A \lor (B land C) = (A \lor B) \land (A \lor C)

.\nThese laws ensure that any complex expression can be reduced to its minimal equivalent form.

Algebraic Simplification Laws