{
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    "id": "yWGTIPMXotxs"
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   "source": [
    "# **Exercise 2. Recursion in positive logic programs.**\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",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "tekDyDF_nJLf"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a:- a, b.\n",
    "b."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **2**"
   ]
  },
  {
   "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",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b, c.\n",
    "b :- a, c.\n",
    "c."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **3**"
   ]
  },
  {
   "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": [
      "b a\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a.\n",
    "b."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a.\n",
    "b :- c.\n",
    "c."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **4**"
   ]
  },
  {
   "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": [
      "b a c\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a.\n",
    "b.\n",
    "c :- a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a.\n",
    "b.\n",
    "c :- a, b.\n",
    "d :- a, b, c."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ho57hy3em9Yi"
   },
   "source": [
    "#### **5**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "j_3LyCQFnE7K",
    "outputId": "8c702cbe-9240-41dd-a812-6349904b5255"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a :- b.\n",
    "b :- c.\n",
    "c :- a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "tekDyDF_nJLf"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a :- b, d.\n",
    "b :- c, e.\n",
    "c :- a, e.\n",
    "d.\n",
    "e :- d."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **6**"
   ]
  },
  {
   "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": [
      "b a c d\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- c.\n",
    "c :- a.\n",
    "d.\n",
    "c :- d."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b, d.\n",
    "b :- c, d.\n",
    "c :- a, d.\n",
    "d.\n",
    "c :- d."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **7**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a.\n",
    "c :- d.\n",
    "d :- c."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b, c.\n",
    "b :- a, d.\n",
    "c :- d.\n",
    "d :- c.\n",
    "d."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **8**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b a d c\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b.\n",
    "b :- a.\n",
    "c :- d.\n",
    "d :- c.\n",
    "c.\n",
    "b :- d."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- b, c, d.\n",
    "b :- a, c, d.\n",
    "c :- d.\n",
    "d :- c.\n",
    "c.\n",
    "b :- d."
   ]
  }
 ],
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