De Morgan's laws

De Morgan’s laws are fundamental in logic and set theory, providing equivalences that are very helpful when working with conditions in code. In TypeScript (or any other programming language), they can be used to simplify boolean expressions, making your code cleaner and easier to understand.

Table of contents#

De Morgan’s Laws Explained#

De Morgan’s laws can be expressed in two main equivalences:

1. $\neg (A \land B) = (\neg A) \lor (\neg B)$
2. $\neg (A \lor B) = (\neg A) \land (\neg B)$

In words:

• The negation of a conjunction is the disjunction of the negations.
• The negation of a disjunction is the conjunction of the negations.

These can be very useful when dealing with complex conditional logic.

TypeScript Examples#

Let’s look at a couple of examples to illustrate De Morgan’s laws.

Example 1: Simplifying Conditions#

Suppose you have a condition where you want to check:
if neither isSunny nor isWarm is true.

Without De Morgan’s law, you might write:

if (!(isSunny && isWarm)) {
  console.log("It is not sunny or warm.");
}
Copy

Using De Morgan’s law, you can simplify this to:

if (!isSunny || !isWarm) {
  console.log("It is not sunny or warm.");
}
Copy

This makes the condition easier to read and understand, as you are directly checking for the negation of each individual condition.

Example 2: Conditional Rendering#

Consider the following scenario where you want to show a message if neither isUserLoggedIn nor hasPermission is true:

const isUserLoggedIn = false;
const hasPermission = false;

if (!(isUserLoggedIn || hasPermission)) {
  console.log("Access denied.");
}
Copy

Applying De Morgan’s law, you can rewrite it as:

if (!isUserLoggedIn && !hasPermission) {
  console.log("Access denied.");
}
Copy

This makes the intent more explicit:
both conditions must be false for the message to be logged.

In simple words…#

De Morgan’s laws are a powerful tool to simplify logical expressions.
They help make your conditions more readable.

By applying these laws, you can reduce the mental load required to understand nested negations and make your TypeScript code much cleaner and maintainable.