Table of Contents

## What is a counterexample example?

An example that disproves a statement (shows that it is false). Example: the statement “all dogs are hairy” can be proved false by finding just one hairless dog (the counterexample) like below.

## What is an example of a conjecture?

Like a hypothesis, but not stated in as formal, or testable, way. So a conjecture is like an educated guess. Example: I heard the sound of a plastic bag, so I conjecture there might be some food!

## What is meant by a conjecture?

(Entry 1 of 2) 1a : inference formed without proof or sufficient evidence. b : a conclusion deduced by surmise or guesswork The criminal’s motive remains a matter of conjecture. c : a proposition (as in mathematics) before it has been proved or disproved.

## How do you solve a counterexample?

How can we identify counterexamples?

- Identify the condition and conclusion of the statement.
- Eliminate choices that don’t satisfy the statement’s condition.
- For the remaining choices, counterexamples are those where the statement’s conclusion isn’t true.

## Can a conjecture be false?

A conjecture is an “educated guess” that is based on examples in a pattern. It is always possible that the next example would show that the conjecture is false. A counterexample is an example that disproves a conjecture.

## How do you prove conjecture?

Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases. Conjectures must be proved for the mathematical observation to be fully accepted.

## What is a reasonable conjecture?

A conjecture is when a person makes a statement or proposition that seems likely to be true. A conclusion is like a judgment or decision reached by reasoning. A justification is like the action made by someone of showing something to be right or reasonable.

## Is a postulates accepted without proof?

A postulate is an obvious geometric truth that is accepted without proof. Postulates are assumptions that do not have counterexamples.