conjecture


Definition of Conjecture

  • Conjecture is a statement that is believed to be true but not yet proved.

Examples of Conjecture

  • The statement "Sum of the measures of the interior angles in any triangle is 180°" is a conjecture.
  • Here is another such conjecture: "If two parallel lines are cut by a transversal, the corresponding angles are congruent."

Solved Example on Conjecture

Sam proposed that "3n + 1 yields a prime number for any even number n." and called it a conjecture. He explained his conjecture using the numbers 2, 4, and 6. He got 7, 13, and 19. Is his proposition a conjecture?
Choices:
A. Yes
B. No
Correct Answer: B
Solution:
Step 1: A conjecture is a statement that is believed to be true but not yet proved or disproved.
Step 2: Sam's proposition is not a conjecture, because for n = 8, 3n + 1 gives 25, which is not a prime number.

Related Terms for Conjecture

  • Statement
  • Inductive Reasoning
  • Proof