DNF types (Disjunctive Normal Form) in PHP - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a simple DNF clause array.

PHP

<?php
$clause = [[1]];
?>

Drag options to blanks, or click blank then click option'

A'A && B'

B'A || B'

C'A && !B'

D'!A || !B'

Attempts:

3 left

💡 Hint

Common Mistakes

Using '||' instead of '&&' inside a clause.

The clause in DNF is a conjunction (AND) of literals, so 'A && B' is correct.

2fill in blank

medium

Complete the code to represent a DNF formula as an array of clauses.

PHP

<?php
$dnf = [
    ['A', 'B'],
    [1]
];
?>

Drag options to blanks, or click blank then click option'

A['A && C']

B['A || C']

C['!A', 'C']

D['!A || C']

Attempts:

3 left

💡 Hint

Common Mistakes

Using combined strings with '||' or '&&' inside a clause.

Each clause is an array of literals combined with AND. So ['!A', 'C'] is a valid clause.

3fill in blank

hard

Fix the error in the code to correctly check if a literal is negated.

PHP

<?php
$literal = '!A';
$isNegated = [1];
?>

Drag options to blanks, or click blank then click option'

Astrpos($literal, '!') === 0

Bstrpos($literal, '!') == 1

Cstrpos($literal, '!') === false

Dstrpos($literal, '!') > 0

Attempts:

3 left

💡 Hint

Common Mistakes

Checking for position 1 or greater instead of 0.

To check if the literal starts with '!', strpos must return 0 (start of string).

4fill in blank

hard

Fill both blanks to create a function that returns true if a clause contains a literal.

PHP

<?php
function containsLiteral(array $clause, string $literal): bool {
    return in_array([1], [2]);
}
?>

Drag options to blanks, or click blank then click option'

A$literal

B$clause

C$literal[0]

D$clause[0]

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the arguments or using incorrect variables.

The function checks if the literal is in the clause array using in_array.

5fill in blank

hard

Fill all three blanks to build a DNF formula and check if it contains a negated literal.

PHP

<?php
$dnf = [
    ['A', 'B'],
    ['!C', 'D']
];

foreach ($dnf as $clause) {
    foreach ($clause as [1]) {
        if (strpos([2], '!') === 0) {
            echo [3] . " is negated\n";
        }
    }
}
?>

Drag options to blanks, or click blank then click option'

A$literal

B$clause

D$clause[0]

Attempts:

3 left

💡 Hint

Common Mistakes

Using the clause array instead of the literal variable inside the loop.

We loop over each literal in a clause, check if it starts with '!', and print the literal.