Get Counterexample Worksheet

An example of a counterexample statement might be: 'All birds can fly.' A counterexample would be the case of ostriches, which are birds that cannot fly. This kind of reasoning can be applied using the Counterexample Worksheet for clarity and to strengthen your understanding.

To make a counterexample, consider the hypothesis or assertion you wish to challenge. Search for an instance that contradicts the assertion directly. By using the Counterexample Worksheet, you can organize your thoughts and present a compelling, clear counterexample that effectively illustrates the issue.

Making a counterexample starts with understanding the general statement you want to dispute. Then, find a specific case that proves this statement wrong. Utilize the Counterexample Worksheet for systematic thinking, ensuring that your counterexample is well-structured and easily understood.

Constructing a counter example involves pinpointing a claim that needs scrutiny. Follow through by selecting an example that contradicts this claim. Our Counterexample Worksheet can be a helpful tool, guiding you in creating a clear and effective counter example that highlights the flaws in the original statement.

To construct a counter-example, first identify the statement you wish to challenge. Next, find a specific instance that demonstrates the statement's falsehood. Use our Counterexample Worksheet to organize your thoughts, ensuring clarity and precision in your example.

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.

A conditional statement can be expressed as If A, then B. A is the hypothesis and B is the conclusion. A counterexample is an example in which the hypothesis is true, but the conclusion is false. If you can find a counterexample to a conditional statement, then that conditional statement is false.

Notice that we have not proved Arthur's conjecture, but only found several examples that hold true. So, at this point, we say that the conjecture is true. Give a counterexample to this statement: Every prime number is an odd number. The only counterexample is the number 2: an even number (not odd) that is prime.

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.