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Geometry Worksheet C Counter Examples Name: Date: Period: Give a counterexample that disproves each conjecture below. 1) No triangles have two sides of the same length. 2) No women have been elected.

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  2. Begin by entering your name in the designated field to identify the document.
  3. For each conjecture listed, provide a counterexample in the space provided. Start with the first conjecture and think critically about scenarios that would disprove it.
  4. After completing the counterexamples, you may need to simplify integer operations provided in the form as part of the review section.
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A conjecture is an “educated guess” that is based on examples in a pattern. A counterexample is an example that disproves a conjecture.

Consider the following statement: If a food is a fruit, then it is an apple. Now, consider this statement: Mango is a food. It is a fruit, but it is not an apple. Therefore, the mango is the counterexample, thereby making the first statement invalid.

A: A counterexample is an example that disproves a statement or conjecture. True or false: A counterexample proves a statement or conjecture to be true.

To show that a conjecture is true, you must show that it is true for all cases. You can show that a conjecture is false, however, by finding just one counterexample. A counterexample is a specific case for which the conjecture is false.

Even if a counterexample is not found, it does not mean that the conjecture is true. It is not possible to try all the possible cases, so it is not possible to prove a conjecture. On the other hand, one counterexample can disprove a conjecture. Once a counterexample has been found, the conjecture is invalid.

A conjecture is a mathematical statement that has not yet been rigorously proved. 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.

Vocabulary Language: English ▼ Spanish English TermDefinitionconjectureA conjecture is an educated guess that is based on examples in a pattern.counterexampleA counterexample is an example that disproves a conjecture.1 more row • Feb 24, 2012

You could prove him wrong, or disprove his conjecture, by offering a counterexample. Say your friend, John, is a guy and does not play sports. Just one counterexample is enough to disprove your brother's conjecture.

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