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?

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.

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