Which of the following boolean expression is related to De-Morgan theorem ?

Question

Prepp Team · Accepted Answer

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).

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. $(xy)' = x' + y'$

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.

The boolean expression that correctly represents De Morgan's theorem is $(x + y)' = x'y'$.

Prepp Team · Answer

$x + xy = x$

Prepp Team · Answer

$x + (y + z) = (x + y) + z$

Prepp Team · Answer

$x(y + z) = xy + xz$

List-I	List-II
Electronic Configuration	First Ionisation energy (kJ mol$^{-1}$)
(A). ns$^2$	(I). 2100
(B). ns$^2$np$^1$	(II). 1400
(C). ns$^2$np$^3$	(III). 800
(D). ns$^2$np$^6$	(IV). 900