question
stringclasses 5
values | choices
sequence | answer
class label 3
classes | negate_openai_prompt
dict | neg_question
stringclasses 5
values | fewshot_context
stringclasses 1
value | fewshot_context_neg
stringclasses 1
value |
|---|---|---|---|---|---|---|
Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field. | [
"0",
"1",
"2",
"3"
] | 1B
| {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n\nNegated text:",
"role": "user"
} | Are there any c in Z_3 such that Z_3[x]/(x^2 + c) is not a field? | ||
Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G. | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 1B
| {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n\nNegated text:",
"role": "user"
} | Statement 1 | If aH is not an element of a factor group, then |aH| does not divide |a|. Statement 2 | If H and K are subgroups of G then HK is not a subgroup of G. | ||
Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements. | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 2C
| {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n\nNegated text:",
"role": "user"
} | Statement 1 | Not every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 does not have 10 elements. | ||
Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian. | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 0A
| {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n\nNegated text:",
"role": "user"
} | Statement 1 | Is it possible for a function from a finite set onto itself to not be one to one?
Statement 2 | Is it possible for a subgroup of an abelian group to not be abelian? | ||
Find the characteristic of the ring 2Z. | [
"0",
"3",
"12",
"30"
] | 0A
| {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Find the characteristic of the ring 2Z.\n\nNegated text:",
"role": "user"
} | What is not the characteristic of the ring 2Z? |