Question

\(a)\)What is the dual of a Boolean expression\(?\)

\(b)\)What is the duality principle\(?\) How can it be used to find new identities involving Boolean expressions\(?\)

Short answer

\((a)\)The dual of a Boolean expression interchanges the sum and product, then interchanges \(0\) and \(1\).

\((b)\)The duality principle states that taking the dual of both sides of an identity results in a new identity that is also valid.

Take dual of each side of an identity, which is in a new identity.

Step-by-step solution

Definition

The dual of a Boolean expression is the obtains by interchanging addition, multiplication and interchanging 0's, 1's.

Using the duality principle

(a)

The dual of a Boolean expression interchanges the sum and product, then interchanges \(0\) and \(1\). Because the dual of a Boolean expression is the obtains by interchanging addition, multiplication and interchanging 0's, 1's.

Applying the duality concept

(b)

The duality principle states that taking the dual of both sides of an identity results in a new identity that is also valid.

Use the duality principle to determine new identities involving Boolean expressions by taking the dual of each side of an identity (which results in new valid identities).