pranavek/set_theory.ipynb

## set_theory.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib_venn import venn2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = {1 ,12 ,30 ,24 ,15} # Set A | |A| = 5\n",
    "B = {1 ,30 ,25} # Set B | |B| = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intersection ∩ {1, 30}\n",
      "Cardinality of A ∩ B is  2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x7febf22fffd0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(A.intersection(B)) #A ∩ B | A new set with elements \"in common\" | {x | x ∈ A and x ∈ B }\n",
    "print('Cardinality of A ∩ B is ', len(A.intersection(B))) #|A ∩ B| \n",
    "venn2([A, B]) # intersection: 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1, 24, 25, 12, 30, 15}\n",
      "Cardinality of A ∪ B is  6\n",
      "Cardinality of A is  5\n",
      "Cardinality of B is  3\n",
      "Cardinality of A ∩ B is  2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x7febf2359e48>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(A.union(B)) #A ∪ B | All elements of either A or B | {x | x ∈ A or x ∈ B }\n",
    "print('Cardinality of A ∪ B is ',len(A.union(B))) #|A ∪ B|\n",
    "print('Cardinality of A is ', len(A)) #|A|\n",
    "print('Cardinality of B is ', len(B)) #|B|\n",
    "print('Cardinality of A ∩ B is ', len(A.intersection(B))) #|A ∩ B|\n",
    "\n",
    "venn2([A, B]) # Union: 3 + 2 + 1 = 6 => |A ∪ B| = |A| + |B| - |A ∩ B| => 5 + 3 - 2 = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set theory in context of clinical trials of COVID-19 test kits\n",
    "X = {'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M'} #Set of partcipants in trail\n",
    "S = {'B', 'E', 'H', 'I', 'J', 'L'} # Sick people S ⊂ X , {x ∈ X: x has COVID-19 }\n",
    "H = {'A', 'C', 'D', 'F', 'G', 'K', 'M'} # Healthy people H ⊂ X, {x ∈  X : x doesn't have COVID-19}\n",
    "v= venn2([S, H])\n",
    "v.get_label_by_id('A').set_text('S') #Override default label\n",
    "v.get_label_by_id('B').set_text('H')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sick people in the clinical trail\n",
    "v = venn2([X, S])\n",
    "v.get_label_by_id('A').set_text('X')\n",
    "v.get_label_by_id('B').set_text('S')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The cardinality of X is  13\n",
      "{'G', 'K', 'J', 'B', 'C', 'H', 'A', 'D', 'E', 'L', 'F', 'I', 'M'}\n",
      "The cardinality of H union S is  13\n"
     ]
    }
   ],
   "source": [
    "print('The cardinality of X is ',len(X)) # |X|\n",
    "print(H.union(S)) # |S ∪ H|\n",
    "print('The cardinality of H union S is ',len(H.union(S))) # |S ∪ H| = |X|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "set()\n",
      "The cardinality of H intersection S is  0\n"
     ]
    }
   ],
   "source": [
    "print(H.intersection(S)) # Intersection of H and S will be empty | A person can be either sick or healty, not both\n",
    "print('The cardinality of H intersection S is ',len(H.intersection(S))) # |H ∩ S| = ∅ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = {'B', 'E', 'A', 'M', 'J', 'L'} # {x ∈ X:  x tests positive for COVID-19 }\n",
    "N = {'H', 'C', 'D', 'F', 'G', 'K', 'I'} # {x ∈ X:  x tests negative for COVID-19 }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|P ∪ N| is 13\n",
      "|P ∩ N| is  0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('|P ∪ N| is', len(P.union(N))) # |P ∪ N| = |X|\n",
    "print('|P ∩ N| is ', len(P.intersection(N))) # |P ∩ N| = ∅ \n",
    "\n",
    "v = venn2([P, N])\n",
    "v.get_label_by_id('A').set_text('P')\n",
    "v.get_label_by_id('B').set_text('N')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# In ideal scenario, S = P  and H = N, however, that's not the case always. \n",
    "# Following sets helps to understand how reliable the test kits are\n",
    "\n",
    "# S ∩ P = {x | x ∈ S and x ∈ P } = True positive\n",
    "v = venn2([S, P])\n",
    "v.get_label_by_id('A').set_text('S')\n",
    "v.get_label_by_id('B').set_text('P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# H ∩ P = {x | x ∈ H and x ∈ P } = False postive\n",
    "v = venn2([H, P])\n",
    "v.get_label_by_id('A').set_text('H')\n",
    "v.get_label_by_id('B').set_text('P') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# S ∩ N = {x | x ∈ S and x ∈ N } = False negative \n",
    "v = venn2([S, N])\n",
    "v.get_label_by_id('A').set_text('S')\n",
    "v.get_label_by_id('B').set_text('N') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# H ∩ N = {x | x ∈ H and x ∈ N } = True negative\n",
    "v = venn2([H, N])\n",
    "v.get_label_by_id('A').set_text('H')\n",
    "v.get_label_by_id('B').set_text('N') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of sick people in the study 0.46153846153846156\n",
      "Proportion of healthy people in the study 0.5384615384615384\n"
     ]
    }
   ],
   "source": [
    "#Rates of test results\n",
    "\n",
    "#|S| / |X| = Proportion of sick people in the study\n",
    "print('Proportion of sick people in the study', len(S)/len(X))\n",
    "\n",
    "#|H| / |X| = Proportion of healthy people in the study\n",
    "print('Proportion of healthy people in the study', len(H)/len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rate of true positive  0.6666666666666666\n",
      "Rate of false positive  0.2857142857142857\n",
      "Rate of false negative  0.3333333333333333\n",
      "Rate of true negative  0.7142857142857143\n"
     ]
    }
   ],
   "source": [
    "# |S ∩ P| / |S| = Rate of true positive \n",
    "# Bigger the rate better the test kits are\n",
    "print('Rate of true positive ',len(S.intersection(P))/len(S))\n",
    "\n",
    "# |H ∩ P| / |H| = Rate of false positive \n",
    "print('Rate of false positive ',len(H.intersection(P))/len(H))\n",
    "\n",
    "# |S ∩ N| / |S| = Rate of false negative\n",
    "print('Rate of false negative ',len(S.intersection(N))/len(S))\n",
    "\n",
    "# |H ∩ N| / |H| = Rate of true negative\n",
    "# If the rates are nearer to value 1, better the test kits are \n",
    "print('Rate of true negative ',len(H.intersection(N))/len(H))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": ".venv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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