What is a statement that is true and false?

A true-false statement is any sentence that is either true or false but not both. A negation of a statement has the opposite meaning of a truth value. If we join two statements we can form a compound statement or a conjunction.

Is the statement This statement is false true?

If (A) is false, then “This statement is false” is false. Therefore, (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.

What is it called when a statement is false?

A false statement is a statement that is not true. Although the word fallacy is sometimes used as a synonym for false statement, that is not how the word is used in philosophy, mathematics, logic and most formal contexts. A lie is a statement that is known to be untrue and is used to mislead.

What is an example of a false statement?

Examples of such words are never, none, always, all, every, entirely and only. These words tend to make a statement false, but not always. ❖ EXAMPLE – Everyone should exercise daily. This statement is false due to the word everyone.

Can something be both true and false at the same time?

Dialetheism (from Greek δι- di- ‘twice’ and ἀλήθεια alḗtheia ‘truth’) is the view that there are statements which are both true and false. Such statements are called “true contradictions”, dialetheia, or nondualisms.

Which statement Cannot be proven at all?

Answer: An axiom is a mathematical statement or property considered to be self-evidently true, but yet cannot be proven. All attempts to form a mathematical system must begin from the ground up with a set of axioms. For example, Euclid wrote The Elements with a foundation of just five axioms.

Which statement is always false?

A statement which is always false is called a contradiction. For example, p ∧ (¬p) is a contradiction, while p ∨ (¬p) is a tautology.

What’s a paradox example?

Here are some thought-provoking paradox examples: Save money by spending it. If I know one thing, it’s that I know nothing. This is the beginning of the end. Deep down, you’re really shallow.

How do you prove a false statement?

To prove a false statement in violation of 18 U.S.C. 1001, the government must show that the defendant: (1) knowingly and willfully, (2) made a statement, (3) in relation to a matter within the jurisdiction of a department or agency of the United States, (4) with knowledge of its falsity. United States v.

What is the legal definition of a false statement?

: a statement that is known or believed by its maker to be incorrect or untrue and is made especially with intent to deceive or mislead submitted a false statement to obtain the loan also : the federal crime of concealing a material fact, making a false statement, or using documents known to be falsified — see also …

What happens if you give a false statement?

Perjury. Perjury involves making false statements while under oath or affirmation. If you lie about something material while giving such testimony, you can be charged with perjury.

What are true or false questions?

A true or false question consists of a statement that requires a true or false response. Effective true or false eLearning questions are factual based, rather than opinion-oriented, and are designed to quickly and efficiently test learner knowledge about a particular idea or concept.

What makes a statement a true or false statement?

So what makes something a statement? Definition: Statements are the kind of sentences that are either true or false. As such, a statement is an assertion that something is or is not the case. A statement is true if what it asserts is the case, and it is false if what it asserts is not the case.

What are examples of something true and false at the same time?

If it is indeed true and everything he says is lie, this makes his statement a truth and it contradict to his statement that everything he says is lie, but if the sentence is false, then he is telling the truth which again contradicts his statement. Think about it. So this is one sentence which is both a truth and a lie at the same time.

What makes a statement a statement in mathematics?

In mathematics, a statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Which is not an example of a statement?

Questions, commands and advice are typically not statements, because they do not express something that is either true or false. But sometimes people use them rhetorically to express statements. We saw an example of a question which by itself is not a statement, but can be used to express a statement.

What happens if a statement is neither true nor false?

The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox: This statement is not true. (B) If (B) is neither true nor false, then it must be not true. Since this is what (B) itself states, it means that (B) must be true.

Is the hypothesis that ( a ) is false a contradiction?

Therefore, (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction. If (A) is false, then “This statement is false” is false. Therefore, (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction.

Is the following sentence true and false at the same time?

The following is the two-sentence version: The following statement is true. (D1) The preceding statement is false. (D2) Assume (D1) is true. Then (D2) is true. This would mean that (D1) is false. Therefore, (D1) is both true and false. Assume (D1) is false. Then (D2) is false. This would mean that (D1) is true. Thus (D1) is both true and false.

Which is true if you assume ( E1 ) is false?

Assume (E1) is false. Then (E2) is true, which means (E3) is false, and hence (E1) is true. Either way, (E1) is both true and false – the same paradox as with (A) and (D1). There are many other variants, and many complements, possible. In normal sentence construction, the simplest version of the complement is the sentence: This statement is true.