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?

  1. Identify the condition and conclusion of the statement.
  2. Eliminate choices that don’t satisfy the statement’s condition.
  3. 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.