dataset_name: formal_logic
description: The following are multiple choice questions (with answers) about formal
  logic.
fewshot_config:
  sampler: first_n
  samples:
  - question: "Which of the given formulas of PL is the best symbolization of the following\
      \ sentence?\nTurtles live long lives and are happy creatures, unless they are\
      \ injured.\n(A) (L \u2022 H) \u2261 I (B) (L \u2022 H) \u2228 I (C) L \u2022\
      \ (H \u2228 I) (D) L \u2022 (H \u2283 R)."
    target: "Let's think step by step. We refer to Wikipedia articles on formal logic\
      \ for help. Let\u2019s solve this step by step. Let \u201CL\u201D denote \u201C\
      living long\u201D, H \u201Cbeing happy\u201D, and \u201CI\u201D \u201Cbeing\
      \ injured\u201D. Now, consider each choice:\n(A) means (living long AND being\
      \ happy) is equivalent to (being injured). \n(B) means (living long AND being\
      \ happy) OR (being injured). \n(C) means (living long) AND (being happy OR being\
      \ injured). \n(D) means (living long) AND (being happy implies being R), but\
      \ what R denotes is not clear.\nObviously, (B) is the best symbolization of\
      \ the original sentence. The answer is (B)."
  - question: 'Select the best translation into predicate logic.George borrows Hector''s
      lawnmower. (g: George; h: Hector; l: Hector''s lawnmower; Bxyx: x borrows y
      from z).

      (A) Blgh (B) Bhlg (C) Bglh (D) Bghl'
    target: "Let's think step by step. We refer to Wikipedia articles on formal logic\
      \ for help. Let\u2019s solve this step by step. We are told that \u201CBxyx\u201D\
      \ means \u201Cx borrows y from z\u201D. We can rewrite \u201CGeorge borrows\
      \ Hector's lawnmower\u201D as \u201CGeorge borrows a lawnmower from Hector\u201D\
      , which can then be translated into predicate logic as \u201CBglh\u201D. The\
      \ answer \u201CBglh\u201D appears in (C); therefore, (C) must be the correct\
      \ answer. The answer is (C)."
  - question: "\nSelect the best English interpretation of the given arguments in predicate\
      \ logic.\nDm\n(\u2200x)(Wx \u2283 ~Dx). \n(\u2200x)Wx \u2228 Ag\t/ (\u2203x)Ax\n\
      (A) Marina is a dancer. Some weaklings are not dancers. Either everything is\
      \ a weakling or Georgia plays volleyball. So something plays volleyball. (B)\
      \ Marina is a dancer. No weakling is a dancer. Everything is either a weakling\
      \ or plays volleyball. So something plays volleyball. (C) Marina is a dancer.\
      \ Some weaklings are not dancers. Everything is either a weakling or plays volleyball.\
      \ So something plays volleyball. (D) Marina is a dancer. No weakling is a dancer.\
      \ Either everything is a weakling or Georgia plays volleyball. So something\
      \ plays volleyball."
    target: "Let's think step by step. We refer to Wikipedia articles on formal logic\
      \ for help. Let\u2019s solve this step by step. Let \u201CD\u201D denote \u201C\
      being a dancer\u201D, \u201Cm\u201D denote \u201CMaria\u201D, \u201Cg\u201D\
      \ denote \u201CGeorgia\u201D, \u201CW\u201D denote \u201Cweakling\u201D, \u201C\
      A\u201D denote \u201Cplaying volleyball\u201D. Then, we have the following:\n\
      1. Dm \u2192 Maria is a dance.\n2. (\u2200x)(Wx \u2283 ~Dx). \u2192 For all\
      \ x, if x is a weakling, then x is not a dancer. In other words, no weakling\
      \ is a dancer.\n3. (\u2200x)Wx \u2228 Ag\t/ (\u2203x)Ax \u2192 For all x, x\
      \ is a weakling or Georgia plays volleyball. So there exists an x that plays\
      \ volleyball. \nOptions (A) and (C) do claim that some weaklings are not dancers,\
      \ but the second argument strongly states that no weakling is a dancer. Thus,\
      \ we can eliminate them. Option (B) omits the important detail about Georgia\
      \ playing volleyball. Option (D) has all the details presented in the arguments\
      \ and is the best English interpretation of the arguments. The answer is (D)."
  - question: "Select the best translation into predicate logic: No people drive on Mars.\n\
      (A) ~Pd (B) (\u2200x)(Px \u2228 ~Dx) (C) (\u2200x)(Px \u2283 ~Dx) (D) ~Dp"
    target: "Let's think step by step. We refer to Wikipedia articles on formal logic\
      \ for help. Let\u2019s solve this step by step. Let \u201CP\u201D denote \u201C\
      being on Mars\u201D and \u201CD\u201D denote \u201Cdriving on Mars\u201D. Then\
      \ let\u2019s consider each option:\nOption (A): ~Pd \u2192 d is not on Mars.\n\
      Option (B): (\u2200x)(Px \u2228 ~Dx) \u2192 For all x, x is on Mars and x do\
      \ not drive on Mars.\nOption (C): (\u2200x)(Px \u2283 ~Dx) \u2192 For all x,\
      \ x is on Mars implies that x do not drive on Mars.\nOption (D): ~Dp: \u2192\
      \ p do not drive on Mars.\nOf all these options, Option (C) appears to be the\
      \ best and most meaningful interpretation of the argument \u201CNo people drive\
      \ on Mars.\u201D The answer is (C).\n\n"
tag: mmlu_flan_cot_fewshot_humanities
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_formal_logic
