{
  "translations": {
    "en": {
      "recall": {
        "type": "select",
        "description":"Let us remind ourselves of some closure properties for regular languages.",
        "question": "Suppose that $L$ is a regular laguage. Which of the following is also regular?",
        "answer": ["Complement of L", "Homomorphism of L", "$L^*$"],
        "choices": ["Complement of L", "Homomorphism of L", "$L^*$"]
      },
      "recall2": {
        "type": "select",
        "description":"Let us remind ourselves of some closure properties for regular languages.",
        "question": "Suppose that $L_1$ and $L_2$ are regular laguages. Which of the following is also regular?",
        "answer": ["$L_1 \\cap L_2$", "$L_1 \\cup L_2$", "$L_1 \\cdot L_2$", "$L_1 - L_2$", "$L_1 / L_2$"],
        "choices": ["$L_1 \\cap L_2$", "$L_1 \\cup L_2$", "$L_1 \\cdot L_2$", "$L_1 - L_2$", "$L_1 / L_2$"]
      },
      "result": {
        "type": "select",
        "description":"<b>Proof outline:</b> Assume $L$ is regular<br/>Apply operations to $L$ that we know are closed for regular languages, and perhaps we include other languages that we know are regular as part of the closed operation. (The goal is to construct $L'$ that you know is non-regular.)",
        "question": "Since we applied a closed operator on $L$, if $L$ is regular then $L'$ must be:",
        "answer": "regular",
        "choices": ["regular", "non-regular"]
      }
    }
  }
}