Does a counterexample always disprove a conjecture?
1 Answer. A counterexample always disproves conjectures. A conjecture will suppose that something is true for different cases, but if you find an example where it is not, the conjecture must be modified to not include a particular case or rejected.
What is contradictory data in qualitative research?
Contradictory evidence, often known as deviant cases, must be sought out, examined, and accounted for in the analysis to ensure that researcher bias does not interfere with or alter their perception of the data and any insights offered.
Does an example always prove a conjecture?
A conjecture is an “educated guess” that is based on examples in a pattern. However, no number of examples can actually prove a conjecture. It is always possible that the next example would show that the conjecture is false. A counterexample is an example that disproves a conjecture.
Does a postulates need to be proven?
In geometry, a postulate is a statement that is assumed to be true based on basic geometric principles. A long time ago, postulates were the ideas that were thought to be so obviously true they did not require a proof. A theorem is a mathematical statement that can and must be proven to be true.
Is a conjecture always true?
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.
What is an example of contradiction?
A contradiction is a situation or ideas in opposition to one another. Examples of a contradiction in terms include, “the gentle torturer,” “the towering midget,” or “a snowy summer’s day.” A person can also express a contradiction, like the person who professes atheism, yet goes to church every Sunday.
How do you prove a contradiction?
To prove something by contradiction, we assume that what we want to prove is not true, and then show that the consequences of this are not possible. That is, the consequences contradict either what we have just assumed, or something we already know to be true (or, indeed, both) – we call this a contradiction.
What is an example that shows a conjecture is not true?
To show that a conjecture is false, you have to find only one example in which the conjecture is not true. It can be a drawing, a statement, or a number. is a statement that can be written in the form “if p, then q.”
What is a conclusion that you reach using inductive reasoning?
A conclusion you reach using inductive reasoning is called a conjecture . Examining several specific situations to arrive at a conjecture is called inductive reasoning. Inductive reasoning is different than proof. It can be used to make predictions, but it should never be used to make certain claims.
What should you do when you find contradicting information in different sources?
What should you do when you find contradicting information in different sources? Believe the facts that support your own opinion. Find and compare additional sources on the topic. Ask an adult to explain which facts are accurate.
Why is proof by contradiction valid?
Proof by contradiction is valid only under certain conditions. The main conditions are: – The problem can be described as a set of (usually two) mutually exclusive propositions; – These cases are demonstrably exhaustive, in the sense that no other possible proposition exists.
Which Cannot be used in a proof?
Undefined terms cannot be used as a proof in geometry. Undefined terms are the words that are not formally defined. The three words in geometry that are not formally defined are point, line, and plane.
What does contradicting mean?
1 : to assert the contrary of : take issue with contradict a rumor She contradicted her brother’s account of what happened. 2 : to imply the opposite or a denial of Your actions contradict your words.