How do you write a counter example?
Asked by: Prof. Dortha Sipes | Last update: June 16, 2025Score: 5/5 (5 votes)
- 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.
What is an example of a counter example?
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.
What is a counter example in an argument?
A counter-example to an argument is a situation which shows that the argument can have true premises and a false conclusion.
How to write a counter example proof?
Therefore: To give a counterexample to a conditional statement P → Q, find a case where P is true but Q is false. Equivalently, here's the rule for negating a conditional: ¬(P → Q) ↔ (P ∧ ¬Q) Again, you need the “if-part” P to be true and the “then-part” Q to be false (that is, ¬Q must be true).
What is a formal counter example?
Formal counterexamples prove that an argument is logically invalid rather than that beliefs are false. An argument is logically valid if it's impossible for the argument structure to have true premises and a false conclusion at the same time.
How to write a good essay: Paraphrasing the question
How to give a counter example?
- 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.
What are good examples of counter arguments?
Examples of the counterargument structure
Some people may rightly argue that if smoking on campus is not illegal, then it should be permitted; however, second-hand smoke may cause harm to those who have health issues like asthma, possibly putting them at risk.
How to create a counterexample?
To make a counterexample in math, first, find an example that satisfies the conditions of the theorem. Then, demonstrate that the example proves the opposite of the conclusion of the theorem.
How do you write a counter statement?
Identify the opposing argument. Respond to it by discussing the reasons the argument is incomplete, weak, unsound, or illogical. Provide examples or evidence to show why the opposing argument is unsound, or provide explanations of how the opposing argument is incomplete or illogical.
How to make a counterexample?
The "counterexample method" is a powerful way of exposing what is wrong with an argument that is invalid. If we want to proceed methodically, there are two steps: 1) Isolate the argument form; 2) Construct an argument with the same form that is obviously invalid. This is the counterexample.
Where do you write a counter argument?
as a section or paragraph just before the conclusion of your essay, in which you imagine what someone might object to what you have argued.
What is an example of counter and counterclaim?
Example- Claim: Cell Phones should be allowed in the classroom. Counterclaim: Cell Phones should not be allowed in the classroom. Rebuttal: By allowing cell phone use in the classroom, students learn how to use and manage their cell phones as a digital resource as they should outside of school.
What is a counter example quizlet?
Counterexample. A counterexample to an argument form is a substitution instance in which the premises are true and the conclusion is false.
What is a good sentence for counter?
Both of them had to counter fierce criticism. The union countered with letters rebutting the company's claims. The Prime Minister countered by stating that he had grave misgivings about the advice he had been given.
What is the least counter example?
In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction.
What is an example of a counter question?
Meaning of counter-question in English
a question that is asked in reply to another question: She answered with a counter-question. To the question "What does it mean?" he poses a counterquestion: "How does it feel?" The best way to answer some questions is with a counter-question.
How to write counterclaims?
Begin the counterclaim paragraph with a topic sentence that acknowledges the opposing side and references the previous paragraph to create a smooth transition. Provide evidence from the opposing side that supports their claim. Rebut the counterclaim.
How do you write a counter offer example?
I would like to propose a counter offer of [Your Counter Offer Salary], which falls within the average salary range for this position in [State]. I want to emphasize my strong interest in the job and my genuine excitement about the opportunity to work with the talented team at [Company], and I'm open to negotiating.
How do you write a counter point?
In first species, write note-against-note counterpoint in whole notes. In second species, write two half notes against a cantus firmus in whole notes. You can begin your counterpoint on the first or third beat of the measures. In third species, write four quarter notes against a cantus firmus in whole notes.
How to prove by counter example?
A counterexample can prove that a statement is false in general because it exhibits one case in which the statement is false. Therefore, we cannot state that the statement is always true. Consider the statement “Every real number has a reciprocal.” We can think of millions of numbers that do have a reciprocal.
What is the counter example method in logic?
The Counter-Example Method: Once you determine the form that an argument has, if you can find an example of an argument with that same form where the premises are true and the conclusion is false, then that argument form is invalid.
How to start a sentence for a counter argument?
- Some people believe/argue/feel/think that…
- It is true that…
- Opposing views claim…
- One common concern about (the issue) is…
- Supporters of….
What are three examples of arguments?
- Liberal arts is best [claim] because it teaches students independent thinking [reason];
- That was Newman's best [claim] because it presented the most difficult role [reason];
- Global warming is real [claim] because the most reputable science points in that direction [reason].
What is a counter example in debate?
An example of a counter argument is the debate about the origins of the Universe. Scientists show that the world was created billions of years ago, although this is debated amongst followers of religion who claim it is merely thousands of years old.