{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an ipython (jupyter) worksheet with code from the lecture notes for the course\n",
    "**Permutation Puzzles: A Mathematical Perspective**, by Jamie Mulholland\n",
    "\n",
    "Coures webpage: http://www.sfu.ca/~jtmulhol/math302 <br />\n",
    "Course notes booklet: http://www.sfu.ca/~jtmulhol/math302/notes/302notes.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lecture 2: Set Theory\n",
    "\n",
    "## 2.4 Examples Using Sage Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1, 2, 3, 4, 5} {3, 4, 5, 6, 7}\n"
     ]
    }
   ],
   "source": [
    "S1=Set([1,2,3,4,5]);\n",
    "S2=Set([3,4,5,6,7]);\n",
    "print S1,S2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S1.cardinality()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 2, 3, 4, 5, 6, 7}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S1.union(S2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{3, 4, 5}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S1.intersection(S2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 2}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S1.difference(S2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{6, 7}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S2.difference(S1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "The Cartesian product of ({1, 2, 3, 4, 5}, {3, 4, 5, 6, 7})"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cartesian_product([S1, S2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 3)\n",
      "(1, 4)\n",
      "(1, 5)\n",
      "(1, 6)\n",
      "(1, 7)\n",
      "(2, 3)\n",
      "(2, 4)\n",
      "(2, 5)\n",
      "(2, 6)\n",
      "(2, 7)\n",
      "(3, 3)\n",
      "(3, 4)\n",
      "(3, 5)\n",
      "(3, 6)\n",
      "(3, 7)\n",
      "(4, 3)\n",
      "(4, 4)\n",
      "(4, 5)\n",
      "(4, 6)\n",
      "(4, 7)\n",
      "(5, 3)\n",
      "(5, 4)\n",
      "(5, 5)\n",
      "(5, 6)\n",
      "(5, 7)\n"
     ]
    }
   ],
   "source": [
    "for i in cartesian_product([S1,S2]):\n",
    "    print i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 in S1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 in S2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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