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Conjecture Statement True Proof Inductive reasoning

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.
The statement "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

Additional Links for Conjecture

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Browse for solved examples below on this Math Dictionary term:

Wisconsin Assessment Curriculum - 2006 > Algebra - 1 > Mathematical Processes > A.12.2-Communicate logical arguments and clearly show • why a result does or does not make sense • why the reasoning is or is not valid • an understanding of the difference between examples that support a conjecture and a proof of the conjecture.

Wisconsin Assessment Curriculum - 2006 > Geometry > Mathematical Processes > A.12.2-Communicate logical arguments and clearly show • why a result does or does not make sense • why the reasoning is or is not valid • an understanding of the difference between examples that support a conjecture and a proof of the conjecture.

South Carolina Assessment Curriculum - 2006 > Geometry > Logical Reasoning and Proof > I.C.4-Use inductive reasoning to formulate a conjecture.

Indiana Assessment Curriculum - 2006 > Geometry > Mathematical Reasoning and Problem Solving > G.8.3-Make conjectures about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

Texas Assessment Curriculum - 2006 > Geometry > The student applies logical reasoning to justify and prove mathematical statements. > G.3.D-Use inductive reasoning to formulate a conjecture.

Arizona Assessment Curriculum - 2006 > Geometry > Structure and Logic - Concept 2: Logic, Reasoning, Arguments, and Mathematical Proof > 5.2.PO 10-Construct a counterexample to show that a given conjecture is false.

Arizona Assessment Curriculum - 2006 > Geometry > Structure and Logic - Concept 2: Logic, Reasoning, Arguments, and Mathematical Proof > 5.2.PO 5-Identify a valid conjecture using inductive reasoning.

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