The dual of a Boolean expression is obtained by interchanging
2013
The dual of a Boolean expression is obtained by interchanging
- A.
Boolean sums and Boolean products
- B.
Boolean sums and Boolean products or interchanging 0’s and 1’s
- C.
Boolean sums and Boolean products and interchanging 0’s & 1’s
- 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):
Scan the expression and replace each OR with AND and each AND with OR.
Replace every 0 with 1 and every 1 with 0.
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.