# What is ‘expendable’ in logic and how to explain ‘tautology’ given this image?

## What is tautology cite example what is meant by tautology in logic?

In mathematical logic, a tautology (from Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is “x=y or x≠y”. Similarly, “either the ball is green, or the ball is not green” is always true, regardless of the colour of the ball.

## How do you prove tautology by logical equivalence?

Two logical statements are logically equivalent if they always produce the same truth value. Consequently, p≡q is same as saying p⇔q is a tautology. Beside distributive and De Morgan’s laws, remember these two equivalences as well; they are very helpful when dealing with implications. p⇒q≡¯q⇒¯pandp⇒q≡¯p∨q.

## How do you prove a statement is a tautology?

If you are given a statement and want to determine if it is a tautology, then all you need to do is construct a truth table for the statement and look at the truth values in the final column. If all of the values are T (for true), then the statement is a tautology.

## What makes something a tautology in logic?

tautology, in logic, a statement so framed that it cannot be denied without inconsistency. Thus, “All humans are mammals” is held to assert with regard to anything whatsoever that either it is not a human or it is a mammal.

## What are 5 examples of tautology?

Examples of Tautology:

• The hot summer sun was scorching.
• I personally made this card for you with my own hands.
• The soggy ground was wet and covered in mud.
• I apologize because I am very sorry that I broke your bowl.
• The teacher assisted me by helping me to complete the math problem.

## What is called tautology?

In literary criticism and rhetoric, a tautology is a statement which repeats an idea, using near-synonymous morphemes, words or phrases, effectively “saying the same thing twice.” Tautology and pleonasm are not consistently differentiated in literature.

## How do you write a tautology?

In grammatical terms, a tautology is when you use different words to repeat the same idea. For example, the phrase, “It was adequate enough,” is a tautology. The words adequate and enough are two words that convey the same meaning.

## Which one of the following is an example of tautology?

For example, saying “the ATM machine” is a tautology, because the M already stands for machine.

## What is tautology in 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”.

## Why is tautology used?

Tautology is a literary device whereby writers say the same thing twice, sometimes using different words, to emphasize or drive home a point. It can be seen as redundancy, a style fault that adds needless words to your idea, statement, or content; or it can be defended as poetic license.

## What is tautology in computer science class 12?

Answer: 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. I think u r in class 11th or 12th.

## What is tautology and contradiction with example?

1. 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.

## What is the difference between tautology and contradiction in logic theory?

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

## Is P → Q → [( P → Q → Q a tautology?

(p → q) ∧ (q → p). (This is often written as p ↔ q). Definitions: A compound proposition that is always True is called a tautology.