Can a true statement also imply the opposite of itself?

Can a statement be both true or false?

Dialetheism (from Greek δι- di- ‘twice’ and ἀλήθεια alḗtheia ‘truth’) is the view that there are statements which are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called “true contradictions”, dialetheia, or nondualisms.

Is every statement either true or false?

every statement is either true or false; these two possibilities are called truth values. An argument in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false.

Can two completely opposite statements both be true?

Two universal categorical propositions with the same subject and predicate are contraries if one is an affirmation and the other a denial. Contraries are of the form “Every S is P” and “No S is P.” Contraries may both be false but cannot both be true.

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Can a statement only be true or false?

A statement is true if what it asserts is the case, and it is false if what it asserts is not the case. For instance, the statement “The trains are always late” is only true if what it describes is the case, i.e., if it is actually the case that the trains are always late.

Can a statement be neither true or false?

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. However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is “neither true nor false”.

Can a sentence be neither true or false?

The answer you are looking for is “undecidable”. What is neither true nor false is called an undecidable proposition. This is about the liar paradox and Gödel’s incompleteness theorems. Every attempt to establish the truth of the first proposition leads to a contradiction in the second.

What do you call a statement that is always true?

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

Is the opposite of a true statement always false?

Negation of a statement – the opposite meaning of a statement. The negation of a false statement is always a true statement. The negation of a true statement is always false.

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Is statement always false?

Contradiction: A statement form which is always false.

Is a statement that is either true or false but not both?

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. A negations is written as ~p.

How do you determine if a statement is true or false?

Approach each statement as if it were true and then determine if any part of the statement is false. Just one false part in a statement will make the entire statement false. For a sentence to be true, every part must be “true”.

What proposition will make a false statement and a true statement true?

A proposition has only two possible values: it is either true or false. We often abbreviate these values as T and F, respectively. Given a proposition p, we form another proposition by changing its truth value.
2.1: Propositions.

p ¯p

What is the truth value of its inverse if both hypothesis and conclusion are false?

If we negate both the hypothesis and the conclusion we get a inverse statement: if a population do not consist of 50% men then the population do not consist of 50% women. The inverse is not true juest because the conditional is true. The inverse always has the same truth value as the converse.

What makes a conditional statement true?

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.

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