{
  "data_source": "DigitalLearningGmbH/MATH-lighteval",
  "prompt": [
    {
      "role": "user",
      "content": "Let $G$ be a finite group with normal subgroups $M$ and $N$ such that $M \\cap N = \\{e\\}$, where $e$ is the identity element. Suppose $G$ has a subgroup of index 2. Must there exist a subgroup of index 2 in $G$ that contains either $M$ or $N$? Let's think step by step and output the final answer within \\boxed{}.\nA part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model."
    }
  ],
  "ability": "math",
  "reward_model": {
    "style": "rule",
    "ground_truth": "Yes"
  },
  "extra_info": {
    "split": "train",
    "index": 30045,
    "question": "Let $G$ be a finite group with normal subgroups $M$ and $N$ such that $M \\cap N = \\{e\\}$, where $e$ is the identity element. Suppose $G$ has a subgroup of index 2. Must there exist a subgroup of index 2 in $G$ that contains either $M$ or $N$? Let's think step by step and output the final answer within \\boxed{}.\nA part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model.",
    "transfer_instruction": "A part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model.",
    "difficulty": 8.0,
    "dataset": "DeepMath-103K"
  }
}