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   "source": [
    "# **Exercise 01. Normal logic programs.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b(1) b(2) a(1) a(2)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X).\n",
    "b(1). b(2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X).\n",
    "b(1). b(2). b(3)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c(1) b(1) b(2) a(1)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), c(X).\n",
    "b(1). b(2). \n",
    "c(1). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), c(X).\n",
    "b(1). b(2). \n",
    "c(1). c(2). c(3)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **3**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c(10) b(1,5) b(2,10) a(2)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X,Y), c(Y).\n",
    "b(1,5). b(2,10).\n",
    "c(10)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X,Y), c(Y).\n",
    "b(1,5). b(2,10).\n",
    "c(10). c(5)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **4**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b(1) b(2) a(2)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), Y=X+1, not b(Y).\n",
    "b(1). b(2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), Y=X+1, not b(Y).\n",
    "b(1). b(3)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **5**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b(1) b(2) c(1) a(2)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), not c(X).\n",
    "b(1). b(2). c(1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), not c(X).\n",
    "b(1). b(2). c(1).\n",
    "b(3). c(2)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **6**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b(1,5) b(2,10) c(10) a(1)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X,Y), not c(Y).\n",
    "b(1,5). b(2,10). c(10)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X,Y), not c(Y).\n",
    "b(1,5). b(2,10)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **7**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c(2) b(1,2) b(2,3) a(1)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X,Y), c(Y).\n",
    "b(1,2). b(2,3). \n",
    "c(2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X,Y), c(Y).\n",
    "b(1,2). b(2,3). \n",
    "c(2). c(3)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **8**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b(1) b(2) b(3) a(3)\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), Y = X+1, not b(Y).\n",
    "b(1). b(2). b(3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "a(X) :- b(X), Y = X+1, not b(Y).\n",
    "b(1). b(5)."
   ]
  }
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