Question

question 2 of 2
select the correct answer from each drop - down menu.
complete the sentences to distinguish between a conjecture, a postulate, and a theorem.
postulates and conjectures are similar in that they both have
that are taken to be true without requiring proof.
proven true.
proven using rigorous application of logic
are statements
submit
reset

Explanation:

1. For the first blank: Postulates are taken as true without proof, and conjectures are statements that have not been proven (they are proposed as true but need proof). So "not been" fits here as postulates and conjectures both have statements that are taken as true without requiring proof (postulates) or are proposed but not proven (conjectures). Wait, re - reading: "Postulates and conjectures are similar in that they both have [blank] proven true." Wait, no, postulates are taken as true without proof (so they haven't been proven in the sense of a theorem), and conjectures are also not proven (they are hypotheses). So the first blank should be "not been" because postulates are assumed true without proof (so not proven), and conjectures are also not proven (they are unproven statements).
2. For the second blank: The second part of the sentence is about what they are. Postulates and conjectures are statements (postulates are statements assumed true, conjectures are statements proposed as true but unproven). So the second blank should be "are statements". Wait, looking at the sentence structure: "Postulates and conjectures are similar in that they both have [first blank] proven true. [second blank] that are taken to be true without requiring proof." Wait, maybe I misread. Let's parse again:

First part: "Postulates and conjectures are similar in that they both have [blank1] proven true." Postulates are not proven (they are axioms, assumed), conjectures are unproven (hypotheses). So "not been" is correct for blank1 (they both have not been proven true in the way a theorem is proven; postulates are assumed, conjectures are unproven).

Second part: "[blank2] that are taken to be true without requiring proof." Postulates are statements taken as true without proof. So blank2 is "are statements".

Wait, the drop - down for the second blank (from the image, though the image is a bit unclear, but the second drop - down is about what they are. So the correct fills are:

First blank: not been

Second blank: are statements

Answer:

First blank: not been

Second blank: are statements