Alongside the logical operators AND and OR, the "negation" operation is also frequently used. It changes a logical value to its opposite. In PHP, negation corresponds to the unary operator !:

<?php

!true; // false
!false; // true

For example, if there's a function that checks whether a number is even, then with negation you can perform a check for oddness:

<?php

function isEven(int $number): bool
{
    return ($number % 2) === 0;
}

var_dump(isEven(10)); // => bool(true)
var_dump(!isEven(10)); // => bool(false)

In the example above, we added ! to the left of the function call and got the opposite action.

Negation lets you express the intended rules in code without writing new functions. If you write !!isEven(10), the code will work even in such a case:

<?php

var_dump((bool) isEven(10)); // => bool(true)

In logic, double negation is equivalent to no negation:

<?php

(bool) true; // true
(bool) false; // false

var_dump((bool) isEven(10)); // => bool(true)
var_dump((bool) isEven(11)); // => bool(false)

! can be combined with && and ||. Among the logical operators it has the highest precedence, so it is applied first:

<?php

!true || true; // (!true) || true   => false || true  => true
!true && false; // (!true) && false  => false && false => false

Parentheses change the order of evaluation:

<?php

!(true || true); // !true  => false
!(true && false); // !false => true

A practical example — a function checks whether a driver can get behind the wheel: a license and sobriety are required:

<?php

function canDrive(bool $hasLicense, bool $isDrunk): bool
{
    return $hasLicense && !$isDrunk;
}

var_dump(canDrive(true, false)); // => bool(true)  (has a license, sober)
var_dump(canDrive(true, true)); // => bool(false) (has a license, but drunk)
var_dump(canDrive(false, false)); // => bool(false) (no license)

Now you know what the operators AND, OR, and ! mean. With their help you'll be able to set compound conditions made of two or more logical expressions.

De Morgan's Laws

When working with complex logical expressions, you sometimes need to invert them or rewrite them in an equivalent form that's easier to read. For this there are De Morgan's laws — two rules that describe how negation distributes over a compound expression:

!(A && B)  is equivalent to  !A || !B
!(A || B)  is equivalent to  !A && !B

The first law: the negation of a conjunction equals the disjunction of the negations. Let's check:

<?php

!(true && false); // !false => true
!true || !false; // false || true => true

The second law: the negation of a disjunction equals the conjunction of the negations:

<?php

!(true || false); // !true => false
!true && !false; // false && true => false

In practice, De Morgan's laws help simplify conditions. For example, instead of !($isAdmin || $isModerator) you can write !$isAdmin && !$isModerator — it reads as "not an administrator and not a moderator".

In a word game, players check whether a word is a palindrome. Implement two functions isPalindrome() and isNotPalindrome() that take a string as input

1. The isPalindrome() function determines whether a word is a palindrome or not. A palindrome is a word that reads the same in both directions.

   <?php
   
   isPalindrome('wow'); // true
   isPalindrome('mom'); // true
   isPalindrome('hexlet'); // false
   
   // Words can be passed to the function in any case
   // Therefore, you must first convert the word to lowercase with strtolower()
   isPalindrome('Wow'); // true

   Expand code

   To reverse a word, use the strrev() function.

2. The isNotPalindrome() function checks that a word is NOT a palindrome:

   <?php
   
   isNotPalindrome('wow'); // false
   isNotPalindrome('mom'); // false
   isNotPalindrome('hexlet'); // true

   Expand code

   To do this, call the isPalindrome() function inside isNotPalindrome() and apply negation.