# Always false vs necessarily false , is it the same?

So “always” is the same as “necessarily” with the necessity being logical necessity. However, when one uses modal logic explicitly the type of necessity considered is usually weaker than logical, physical, metaphysical, etc. So “necessarily” has a different meaning.

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## What is it called when a statement 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.

## What is a statement that is either true or false?

Proposition is simply a statement that is either true or false, has no variables involved. But predicates can take variables, and once we replace the variable by a constant, it becomes a proposition.

## What is a statement that is neither true nor 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.

## Are all propositions true or false?

A proposition (statement or assertion) is a sentence which is either always true or always false.

## Is a statement that is always false?

Contradiction: A statement form which is always false.

## Is a statement always true?

The same statement can be true on some occasions and false in others. That is, statements are not always true or always false.

## Is any meaningful statement that is either true or false but never false?

A proposition is a declarative sentence that is either true or false (but not both).

## Is paradox True or false?

A paradox is a logically self-contradictory statement or a statement that runs contrary to one’s expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.

## What compound proposition is always false?

A compound proposition that is always false is called a contradiction. A proposition that is neither a tautology nor contradiction is called a contingency. Example: p ∧ ¬p is a contradiction.

## What does P ∨ Q mean?

P or Q

P ∨ Q means P or Q. An argument is valid if the following conditional holds: If all the premises are true, the conclusion must be true.

## What does P → Q mean?

p → q (p implies q) (if p then q) is the proposition that is false when p is true and q is false and true otherwise. Equivalent to —not p or q“ Ex. If I am elected then I will lower the taxes.

## What is the difference between tautologies and contradiction with example?

A tautology is a statement that is true in virtue of its form. Thus, we don’t even have to know what the statement means to know that it is true. In contrast, a contradiction is a statement that is false in virtue of its form.
2.10: Tautologies, Contradictions, and Contingent Statements.

A B (A v B) ⋅ (~A ⋅ ~B)
T F T F F F T
F T T F T F F
F F F F T F T

## Is P ∧ Q → Pa contradiction?

A statement that is always false is known as a contradiction. Example: Show that the statement p ∧∼p is a contradiction.
Solution:

p ∼p p ∧∼p
T F F
F T F

## Is fallacy and contradiction same?

The contradiction is just the opposite of tautology. When a compound statement formed by two simple given statements by performing some logical operations on them, gives the false value only is called a contradiction or in different terms, it is called a fallacy.

## Can a tautology be false?

In other words it cannot be false. It cannot be untrue. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically contingent.

## What do you call a compound proposition that is neither always true nor always false?

A compound proposition is called a contradiction if it is always false, no matter what the truth values of the propositions (e.g., p A ¬p =T no matter what is the value of p. Why?). Finally, a proposition that is neither a tautology nor a contradiction is called a contingency.

## What is the difference between tautology and pleonasm?

Difference between pleonasm and tautology
Pleonasm has a sense of using an unnecessary overabundance of redundant words in one description. Tautology has a sense of saying the exact same in different words, using multiple words with the same meaning.