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.

Contents

## 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.