In worlds where the classical logic obtains the law of excluded middle will be a tautology, but not in intuitionistic worlds. Thus, **the law of excluded middle will not be a necessary tautology**. Zalta discusses more examples in Logical and Analytic Truths That Are Not Necessary.

## Can a tautology be all false?

A tautology , or tautologous proposition , has a logical form that **cannot possibly be false** (no matter what truth values are assigned to the sentence letters).

## Can a tautology be proven true or false?

A Tautology is a statement that is always true because of its structure—**it requires no assumptions or evidence to determine its truth**. A tautology gives us no genuine information because it only repeats what we already know.

## Are all tautologies logically true?

Note that **every tautology is also a logical truth**, and every logical truth is also a TW-necessity. But the converse is not true: some logical truths are not tautologies, and some TW-necessities are not logical truths.

## Is a tautology true for every value or false for every value?

A Tautology is a formula which is **always true** for every value of its propositional variables.

## Are tautologies valid?

It is not originally defined in the context of premise-conclusion as you said. However, it can be proven that tautological sentences as defined previously is always the ‘true conclusion’ of any argument regardless of truth of the premises. Therefore, **tautology is always valid**.

## What is tautological fallacy?

**The fallacy of using a definition that seems to be sharp and crisp, but is in fact tautological** (but this is hidden, mostly unintentionally). The problem: the point at which a definition that was useful and very sharply defined becomes tautological is often not easily seen.

## How do you determine if a statement is a tautology without truth table?

One way to determine if a statement is a tautology is to **make its truth table and see if it (the statement) is always true**. Similarly, you can determine if a statement is a contradiction by making its truth table and seeing if it is always false.

## How do you verify a tautology?

If you are given any statement or argument, you can determine if it is a tautology by **constructing a truth table for the statement and looking at the final column in the truth table**. If all of the truth values in the final column are true, then the statement is a tautology.

## What makes a statement a tautology?

A tautology is a compound statement in Maths which **always results in Truth value**. It doesn’t matter what the individual part consists of, the result in tautology is always true. The opposite of tautology is contradiction or fallacy which we will learn here.

## Why P ∨ Q ∧ Q ∨ R ∧ R ∨ P is true when P Q and R have the same truth value and it is false otherwise?

Originally Answered: Explain, without using a truth table, why (p ∨￢q) ∧ (q ∨￢r) ∧ (r ∨￢p) is true when p, q, and r have the same truth value and it is false otherwise ? The very short answer is that **a disjunction is true, except when both sides are false and a conjunction is true only when both sides are true**.

## How do you prove or disprove using the truth table?

Easy, by creating a massive truth table that compares the two final columns of both statements. We first calculate the individual truth & false values of both Statement #1 & Statement #2; then, afterwards, compare these final values in order to prove (or disprove) that they’re logically equivalent.

## What is tautology truth table?

A tautology is **a formula which is “always true”** — that is, it is true for every assignment of truth values to its simple components. You can think of a tautology as a rule of logic. The opposite of a tautology is a contradiction, a formula which is “always false”.

## What are tautologies and contradictions?

A tautology is an assertion of Propositional Logic that is true in all situations; that is, it is true for all possible values of its variables. A contradiction is an assertion of Propositional Logic that is false in all situations; that is, it is false for all possible values of its variables.

## Is statement always false?

Contradiction: A statement form which is always false.

## What is the main difference between tautology and contradiction?

**A compound statement which is always true is called a tautology , while a compound statement which is always false is called a contradiction** .

## Could a sentence which is a contradiction ever be a tautology?

**A conditional sentence with a TT-contradiction as its antecedent is a tautology**. That’s because a conditional comes out true on every row in which its antecedent is false. But if the antecedent is a TT-contradiction, it’s false on every row. So the conditional is true on every row, i.e., is a tautology.

## What is a proposition that is 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.