Question

select the correct answer from each drop - down menu.
which are the best definitions for theorem, conjecture, and axiom?
a statement that is assumed to be true without proof is a(n)

. a statement that has been shown to be true by vigorous applica
in logic is a(n)

. a(n)

is a statement that is believed to be true but hasnt been proven.

Explanation:

1. For the first blank: A statement assumed true without proof in logic is an "axiom".
2. For the second part (after "A(n)"): A statement believed true but not proven is a "conjecture" (though the first blank's correct term for the unproven - assumed true is axiom, and the description for conjecture matches "believed true but not proven"). Wait, re - checking:

• Axiom: A statement assumed true without proof.
• Conjecture: A statement believed to be true but not yet proven.
• Theorem: A statement proven true by rigorous application of logic.

So the first drop - down (the one with the first blank) should be "axiom", and the second (the one related to the description "believed to be true but hasn't been proven") is "conjecture". And the last part (the statement proven by rigorous logic) is "theorem". But from the given blanks:

• The first blank: "A statement that is assumed to be true without proof is a(n) [first drop - down]". So first drop - down: axiom.
• Then "A(n) [second drop - down] is a statement that is believed to be true but hasn't been proven." So second drop - down: conjecture.
• And "A statement that has been shown to be true by vigorous applic[ation of logic] is a theorem" (though not fully visible, the pattern is clear).

Answer:

First drop - down: axiom
Second drop - down: conjecture