The dual of a Boolean expression is obtained by interchanging

2013

The dual of a Boolean expression is obtained by interchanging

  1. A.

    Boolean sums and Boolean products

  2. B.

    Boolean sums and Boolean products or interchanging 0’s and 1’s

  3. C.

    Boolean sums and Boolean products and interchanging 0’s & 1’s

  4. D.

    Interchanging 0’s and 1’s

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Correct answer: C

Definition: The dual of a Boolean expression is obtained by simultaneously interchanging Boolean sums (OR) and Boolean products (AND), and by interchanging the constants 0 and 1.

  • Replace every OR ( + ) with AND ( · ), and every AND ( · ) with OR ( + ).

  • Swap the constants 0 and 1.

  • Do not change variables or their complements (negations) when forming the dual.

How to apply (step-by-step):

  1. Scan the expression and replace each OR with AND and each AND with OR.

  2. Replace every 0 with 1 and every 1 with 0.

  3. Leave variable names and complements unchanged.

Examples:

  • Dual of x + 0 is x · 1 (replace + with · and 0 with 1).

  • Dual of x · (y + 0) is x + (y · 1) (replace · with +, + with ·, and 0 with 1).

Note: The dual operation is mechanical — apply the replacements consistently. Do not complement variables unless a complement is already present in the original expression.

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