Math Implies

This package facilitates the solution of discrete mathematical problems.

How to install

composer require noorani-mm/math-implies

How to use

Provide your desired logical statement as the parameter to the Implies class.

$implies = new \Math\Implies\Implies('p->q');

From now on, you can retrieve the required outputs.

---

Table

It constructs a truth table by placing the column headers in the first row and sequentially adding rows to represent logical conditions.

$result = $implies->table
/**
[
  ["p",     "q",  "(p -> q)"], This is columns and others are value
  ["0",     "0",     "1"    ],
  ["0",     "1",     "1"    ],
  ["1",     "0",     "0"    ],
  ["1",     "1",     "1"    ],
]
 */

Columns

It displays the computed logical expressions.

$test1 = $implies->columns(); // ['p', 'q', '(p -> q)']
$test2 = $implies->columns;   // ['p', 'q', '(p -> q)']

Rows

It returns the result of the truth table computation.

$test1 = $implies->rows(); // ["001", "011", "100", "111"]
$test2 = $implies->rows;   // ["001", "011", "100", "111"]

PDNF

The pdnf function returns a string representing the sum of products of the logical statement, obtained by multiplying the components of the logical expression.

Meanwhile, the pdnf property returns an array representing individual product terms of the logical expression, where each element corresponds to a specific term obtained by multiplying the components of the logical statement.

$string = $implies->pdnf(); // "(~p^~q)v(~p^q)v(p^q)"
$array  = $implies->pdnf;   // ["(~p^~q)", "(~p^q)", "(p^q)"]

PCNF

The pcnf function returns a string representing the Product of Sums Normalized (PCNF) for a logical statement by adding its components.

Meanwhile, the pcnf property returns an array representing individual sum terms of the logical expression, with each element corresponding to a specific term obtained by adding the components of the logical statement.

$string = $implies->pcnf(); // "(pv~q)"
$array  = $implies->pcnf;   // ["(pv~q)"]

minterm

The minterm function computes minterms for a logical statement, providing a summarized string representation. The minterm property returns an array of individual minterms, enhancing clarity on the logical conditions.

$string = $implies->minterm(); // "Σ(0,1,3)"
$array  = $implies->minterm;   // [0,1,3];

maxterm

The maxterm function calculates maxterms for a logical statement, presenting a concise string representation. The maxterm property returns an array of individual maxterms, contributing to a clear understanding of the logical conditions.

$string = $implies->maxterm(); // "π(2)"
$array  = $implies->maxterm;   // [2]