test_time_scaling/data/model_method/abstract_algebra/question_0010.json

{
  "question": "Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.",
  "options": {
    "A": "True, True",
    "B": "False, False",
    "C": "True, False",
    "D": "False, True"
  },
  "answer": "C",
  "topk_tokens": [
    "Subgroup",
    "Cosets",
    "Lagrange's Theorem"
  ],
  "uncertainties": [
    null,
    null,
    null
  ],
  "raw_output": "Concepts are fundamental to understanding the problem at hand. For this question, the key concepts are:\n\n{\"concepts\": [\"Subgroup\", \"Cosets\", \"Lagrange's Theorem\"]}"
}