De Morgan’s Laws are fundamental rules in mathematical logic that describe the relationships between the logical operators AND ($∧$) and OR ($∨$). These laws are named after the British mathematician Augustus De Morgan.
🌐 De Morgan’s Laws
There are two main De Morgan’s Laws:

The negation of a conjunction is equivalent to the disjunction of the negations: $¬(A∧B)≡(¬A)∨(¬B)$ This means that “not (A and B)” is equivalent to “(not A) or (not B)“.

The negation of a disjunction is equivalent to the conjunction of the negations: $¬(A∨B)≡(¬A)∧(¬B)$ This means that “not (A or B)” is equivalent to “(not A) and (not B)“.
🚀 Examples in JavaScript
Let’s see how these laws can be applied inJavaScript.
Example 1: Negation of a Conjunction
De Morgan’s Law: $¬(A∧B)≡(¬A)∨(¬B)$
Example 2: Negation of a Disjunction
De Morgan’s Law: $¬(A∨B)≡(¬A)∧(¬B)$
Explanation

Negation of a Conjunction:
 In the
example1
function, we check if the negation of the conjunction of twoboolean values is equivalent to the disjunction of their negations. (a && b)
returnstrue
only if botha
andb
aretrue
. The negation of this expression will betrue
only if at least one of the values isfalse
.(!a  !b)
istrue
if at least one ofa
orb
isfalse
.
 In the

Negation of a Disjunction:
 In the
example2
function, we check if the negation of the disjunction of two boolean values is equivalent to the conjunction of their negations. (a  b)
returnstrue
if at least one ofa
orb
istrue
. The negation of this expression will betrue
only if botha
andb
arefalse
.(!a && !b)
is `true
 In the
true
if both a
and b
are false
.
In both cases, the functions return true
if De Morgan’s Laws hold, demonstrating the equivalence of the expressions as described by the laws.
ℹ️ Conclusion
De Morgan’s Laws are powerful tools in logic and computer science, simplifying complex logical expressions and helping to understand the relationships between logical operations. By applying these laws, we can transform and simplify expressions, making our code more readable and efficient.
Understanding and using De Morgan’s Laws is essential for anyone working with logic, whether in mathematics, computer science, or everyday problemsolving.