## What is difference between logical and equivalence?

**Logical equivalence is different from material equivalence**. Formulas P and Q are logically equivalent if and only if the statement of their material equivalence (P ↔ Q) is a tautology. There is a difference between being true and being a tautology.

## What is the meaning of logical equivalence?

Logical equivalence is **a type of relationship between two statements or sentences in propositional logic or Boolean algebra**. The relation translates verbally into “if and only if” and is symbolized by a double-lined, double arrow pointing to the left and right ( ).

## What is logical equivalence in philosophy?

Logical equivalence. Definition: **a pair of sentences are logically equivalent if and only if it is not possible for one of the sentences to be true while the other sentence is false**. A pair of sentences may turn out true under exactly the same circumstances.

## What does logically equivalent mean example?

Two expressions are logically equivalent **provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions**. In this case, we write X≡Y and say that X and Y are logically equivalent.

## What is equivalence and laws of 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.

## Can two false sentences be logically equivalent?

**No two false sentences are logically equivalent**. circumstances. A pair of equivalent sentences must both be false at the same time if they are false at all.

## Why is logical equivalence important?

**Because tautologies and contradictions are essential in proving or verifying mathematical arguments**, they help us to explain propositional equivalences — statements that are equal in logical argument. And it will be our job to verify that statements, such as p and q, are logically equivalent.

## What is logically equivalent to an IF THEN statement?

A conditional statement is logically equivalent to **its contrapositive**. Converse: Suppose a conditional statement of the form “If p then q” is given. The converse is “If q then p.” Symbolically, the converse of p q is q p.

## What is logically equivalent to P and Q?

The propositions are equal or logically equivalent if they always have the same truth value. That is, p and q are logically equivalent **if p is true whenever q is true, and vice versa, and if p is false whenever q is false, and vice versa**.

Logical Arguments as Compound Propositions.

p | q | [(p → !q) & (!p) ] → q |
---|---|---|

F | F | F |

## What makes two statements logically equivalent?

Two statement forms are logically equivalent if, and only if, **their resulting truth tables are identical for each variation of statement variables**. p q and q p have the same truth values, so they are logically equivalent.

## How do you find the logical equivalence without truth tables?

Quote from the video:

Youtube quote: *So there's a complete proof that the negation of P implies not Q is actually equivalent to P and Q.*