{
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    "id": "yWGTIPMXotxs"
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   "source": [
    "# **Exercise 06. Logic programs with choice rules.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ho57hy3em9Yi"
   },
   "source": [
    "#### **1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "j_3LyCQFnE7K",
    "outputId": "8c702cbe-9240-41dd-a812-6349904b5255"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "a\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a }."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: There is an empty line in the output. It represents the empty stable model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{a} :- b.\n",
    "b."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c\n",
      "a b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a }.\n",
    "b :- a.\n",
    "c :- not a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a }.\n",
    "b :- a.\n",
    "b :- not a."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **3**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "a\n",
      "b\n",
      "b a\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a }.\n",
    "{ b }."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a } :- c.\n",
    "{ b } :- d.\n",
    "c.\n",
    "d :- c."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **4**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "a\n",
      "a b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a }.\n",
    "{ b } :- a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a }.\n",
    "{ b } :- c.\n",
    "c :- a."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ho57hy3em9Yi"
   },
   "source": [
    "#### **5**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "j_3LyCQFnE7K",
    "outputId": "8c702cbe-9240-41dd-a812-6349904b5255"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "c\n",
      "a\n",
      "a b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "{ a }.\n",
    "{ b } :- a.\n",
    "{ c } :- not a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "tekDyDF_nJLf"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "{ a }.\n",
    "{ b } :- d.\n",
    "{ c } :- not d.\n",
    "d :- a."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **6**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c\n",
      "b\n",
      "a\n",
      "a b d\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    "c :- not a, not b.\n",
    "d :- a, b."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    "c :- not a, b.\n",
    "d :- a, not b."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **7**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "a b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    "b :- a.\n",
    "a :- b."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b; c }.\n",
    "b :- a.\n",
    "a :- c.\n",
    "c :- b."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **8**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "c\n",
      "a b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    "b :- a.\n",
    "a :- b.\n",
    "{ c } :- not a, not b."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    "b :- a.\n",
    "a :- b.\n",
    "{ c } :- a, b."
   ]
  }
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