Question

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? %C2%A0(1 point) Responses A definition is a statement that is made based on observations that must be proven true.%C2%A0 A definition is a statement that is made based on observations that must be proven true.%C2%A0 A theorem is assumed to be true, and it does not have to be proven.%C2%A0 A theorem is assumed to be true, and it does not have to be proven.%C2%A0 A postulate is assumed to be true, and it does not have to be proven.%C2%A0 A postulate is assumed to be true, and it does not have to be proven.%C2%A0 A conjecture tells you what a term means or what to do with a concept.

Answer 1

To accurately represent the distinguishing features of the terms mentioned, here are the correct definitions:

- A **definition** is a statement that explains the meaning of a term or concept.
- A **theorem** is a statement that has been proven to be true based on previously established statements, such as postulates or other theorems.
- A **postulate** (or axiom) is a statement assumed to be true without proof, serving as a foundational basis for reasoning within a mathematical system.
- A **conjecture** is a statement that is believed to be true based on observations but has not yet been proven.

Therefore, among the options you've presented, the statement "A postulate is assumed to be true, and it does not have to be proven." accurately represents the distinguishing feature of a postulate. The option regarding definitions and conjectures is incorrect.