9 verdades e 1 mentira, testadas usando pythonlogica

9verdades1mentira.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:14ff5380923bc062ffa073f35da931eac6cb61f1f86d0d3ed028dcef4d274e5e"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Imagem recebida via Internet](http://i.imgur.com/vB66nRk.jpg)\n",
      "\n",
      "9 verdades e 1 mentira:\n",
      "\n",
      "1. P \u2192 (P \u2228 Q)\n",
      "2. (P \u2227 Q) \u2192 P\n",
      "3. (P \u2227 (P \u2192 Q)) \u2192 Q\n",
      "4. \u00ac(P \u2192 Q) \u2192 (P \u2227 \u00acQ)\n",
      "5. (P \u2192 Q) \u2192 (\u00acQ \u2192 \u00acP)\n",
      "6. ((P \u2228 Q) \u2227 \u00acP) \u2192 Q\n",
      "7. ((P \u2192 Q) \u2227 Q) \u2192 P\n",
      "8. ((P \u2228 \u00acQ) \u2227 Q) \u2192 P\n",
      "9. ((P \u2227 Q) \u2227 (P \u2192 R) \u2227 (\u00acQ \u2228 S)) \u2192 (R \u2227 S)\n",
      "10. ((A \u2228 B) \u2227 (C \u2228 \u00acB)) \u2192 (A \u2228 C)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# https://github.com/denilsonsa/pythonlogica\n",
      "from logica import *\n",
      "import string\n",
      "criar_simbolos_no_namespace(string.ascii_uppercase, globals())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predicados = [\n",
      "    P > (P | Q),\n",
      "    (P & Q) > P,\n",
      "    (P & (P > Q)) > Q,\n",
      "    ~(P > Q) > (P & ~Q),\n",
      "    (P > Q) > (~Q > ~P),\n",
      "    ((P | Q) & ~P) > Q,\n",
      "    ((P > Q) & Q) > P,\n",
      "    ((P | ~Q) & Q) > P,\n",
      "    ((P & Q) & (P > R) & (~Q | S)) > (R & S),\n",
      "    ((A | B) & (C | ~B)) > (A | C)\n",
      "]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i, expr in enumerate(predicados):\n",
      "    print(\"{0:>2}. {1!s:<10} {2!s}\".format(i + 1, expr.formula().tautologia(), expr))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1. Verdadeiro (~ P | (P | Q))\n",
        " 2. Verdadeiro (~ (P & Q) | P)\n",
        " 3. Verdadeiro (~ (P & (~ P | Q)) | Q)\n",
        " 4. Verdadeiro (~ ~ (~ P | Q) | (P & ~ Q))\n",
        " 5. Verdadeiro (~ (~ P | Q) | (~ ~ Q | ~ P))\n",
        " 6. Verdadeiro (~ ((P | Q) & ~ P) | Q)\n",
        " 7. Falso      (~ ((~ P | Q) & Q) | P)\n",
        " 8. Verdadeiro (~ ((P | ~ Q) & Q) | P)\n",
        " 9. Verdadeiro (~ (((P & Q) & (~ P | R)) & (~ Q | S)) | (R & S))\n",
        "10. Verdadeiro (~ ((A | B) & (C | ~ B)) | (A | C))\n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}