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. A postulate is assumed to be true, and it does not have to be proven
b. A conjecture tells you what a term means or what to do with a concept
c. A definition is a statement that is made based on observation that must be proven true
d. A theorem is assumed to be true, and it does not have to be proven

Answer 1

The answer choice that accurately represents the term's distinguishing feature is:

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

Here's a brief explanation of the other terms:

• Conjecture: A conjecture is a statement that is believed to be true based on observations, but it has not yet been proven.

• Definition: A definition specifies the meaning of a term or concept and explains what it is, rather than being an observation or needing proof.

• Theorem: A theorem is a statement that has been proven to be true based on previously established truths (such as postulates and other theorems).

Therefore, options b, c, and d do not correctly define their respective terms.