Question
Which of the following boolean expression is related to De-Morgan theorem ?
The correct answer is
$(x + y)' = x'y'$
De Morgan's Theorem Identification
De Morgan's theorem is a fundamental principle in Boolean algebra related to the negation of logical operations (AND, OR).
De Morgan's Laws
- Law 1: The complement of a sum is the product of the complements. $(x + y)' = x'y'$
- Law 2: The complement of a product is the sum of the complements. $(xy)' = x' + y'$
Analyzing the Options
Let's examine each option to see which one matches De Morgan's theorem:
- Option 1: $x + xy = x$ This is the Absorption Law in Boolean algebra.
- Option 2: $x + (y + z) = (x + y) + z$ This is the Associative Law for the OR operation.
- Option 3: $x(y + z) = xy + xz$ This is the Distributive Law.
- Option 4: $(x + y)' = x'y'$ This expression directly matches Law 1 of De Morgan's theorem.
Conclusion
The boolean expression that correctly represents De Morgan's theorem is $(x + y)' = x'y'$.
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Important Questions from Miscellaneous
- Which of the following scheduler/schedulers is/are also called CPU scheduler ?
(A). Short Term Scheduler
(B). Long Term Scheduler
(C). Medium Term Scheduler
(D). Asymmetric Scheduler
Choose the correct answer from the options given below: - A situation where two or more processes are blocked, waiting for resources held by each other is called:
- External fragmentation occurs ________.
- Which disk scheduling algorithm looks for the track closest to the current head position?
- Which CPU scheduling algorithm prefers the process with the shortest burst time?
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