Electrical Engineering XYZ MCQs
The Boolean algebra is mostly based on:
- De Morpan’s theorem
- Boolean theorem
- Standard theorem
- De Morgan’s theorem
Correct answer: 4. De Morgan’s theorem
Explanation: Boolean algebra is a mathematical structure that deals with binary variables and logical operations. De Morgan’s theorem is a fundamental concept in Boolean algebra that provides a relationship between the logical operators “AND,” “OR,” and “NOT.” The theorem is named after Augustus De Morgan, a 19th-century mathematician and logician.
De Morgan’s theorem states two important rules:
- The negation of a conjunction (AND) is equivalent to the disjunction (OR) of the negations of the individual propositions: ¬(A ∧ B) = ¬A ∨ ¬B.
- The negation of a disjunction (OR) is equivalent to the conjunction (AND) of the negations of the individual propositions: ¬(A ∨ B) = ¬A ∧ ¬B.
These rules are crucial in simplifying Boolean expressions and manipulating logic gates in digital circuit design. Therefore, De Morgan’s theorem is a fundamental basis for Boolean algebra, and understanding it is essential for working with Boolean logic and digital systems.