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?

Question

A theorem is assumed to be true, and it does not have to be proven.

A definition is a statement that is made based on observations that must be proven true.

A postulate is assumed to be true, and it does not have to be proven.

A conjecture tells you what a term means or what to do with a concept.

Answer 1

The accurate statement that represents the distinguishing feature of the terms is:

A postulate is assumed to be true, and it does not have to be proven.

Here’s a brief explanation of each term for clarity:

• Postulate: A statement that is accepted as true without proof; it serves as a foundational building block in a mathematical theory.
• Definition: A precise statement that explains the meaning of a term or a concept.
• Conjecture: An educated guess or hypothesis that has not yet been proven or disproven.
• Theorem: A statement that has been proven to be true through logical reasoning and previously established statements, such as axioms and other theorems.

The other answer choices inaccurately describe the characteristics of definitions, conjectures, and theorems.