Asked by mom
Postulates, definitions, conjectures, and theorems each have distinguishing features that help identify them. Which of the following answer choices accurately represents the term’s distinguishing feature? Like which one is the most accurate
Responses
A postulate is assumed to be true, and it does not have to be proven.
A postulate is assumed to be true, and it does not have to be proven. - no response given
A definition is a statement that is made based on observations that must be proven true.
A definition is a statement that is made based on observations that must be proven true. - no response given
A conjecture tells you what a term means or what to do with a concept.
A conjecture tells you what a term means or what to do with a concept. - no response given
A theorem is assumed to be true, and it does not have to be proven.
Responses
A postulate is assumed to be true, and it does not have to be proven.
A postulate is assumed to be true, and it does not have to be proven. - no response given
A definition is a statement that is made based on observations that must be proven true.
A definition is a statement that is made based on observations that must be proven true. - no response given
A conjecture tells you what a term means or what to do with a concept.
A conjecture tells you what a term means or what to do with a concept. - no response given
A theorem is assumed to be true, and it does not have to be proven.
Answers
Answered by
GPT-4o mini
To evaluate the responses and identify the most accurate terms and their distinguishing features, let's analyze each statement:
1. **A postulate is assumed to be true, and it does not have to be proven.**
This statement is accurate. A postulate (or axiom) is accepted as a foundational truth within a given mathematical framework without requiring proof.
2. **A definition is a statement that is made based on observations that must be proven true.**
This statement is inaccurate. A definition does not require proof; it simply explains the meaning of a term or concept. Definitions are often established to clarify terms but do not assert truths that need to be proven.
3. **A conjecture tells you what a term means or what to do with a concept.**
This statement is also inaccurate. A conjecture is an unproven statement or hypothesis that is based on observations, and it may suggest a relationship or property that is yet to be proven. It does not define what a term means.
4. **A theorem is assumed to be true, and it does not have to be proven.**
This statement is inaccurate. A theorem is a statement that has been proven based on previously established statements, such as axioms or other theorems.
Based on this analysis, the most accurate response is:
**A postulate is assumed to be true, and it does not have to be proven.**
1. **A postulate is assumed to be true, and it does not have to be proven.**
This statement is accurate. A postulate (or axiom) is accepted as a foundational truth within a given mathematical framework without requiring proof.
2. **A definition is a statement that is made based on observations that must be proven true.**
This statement is inaccurate. A definition does not require proof; it simply explains the meaning of a term or concept. Definitions are often established to clarify terms but do not assert truths that need to be proven.
3. **A conjecture tells you what a term means or what to do with a concept.**
This statement is also inaccurate. A conjecture is an unproven statement or hypothesis that is based on observations, and it may suggest a relationship or property that is yet to be proven. It does not define what a term means.
4. **A theorem is assumed to be true, and it does not have to be proven.**
This statement is inaccurate. A theorem is a statement that has been proven based on previously established statements, such as axioms or other theorems.
Based on this analysis, the most accurate response is:
**A postulate is assumed to be true, and it does not have to be proven.**
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