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."
Video Examples: Making and Proving Conjectures
Solved Example on Conjecture
Ques: 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?
Correct Answer: B
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.