# What is the law of logical equivalence?

## What is the law of logical equivalence?

Two statements are logically equivalent if, and only if, their resulting forms are logically equivalent when identical statement variables are used to represent component statements.

## What is logical equivalence examples?

Now, consider the following statement: If Ryan gets a pay raise, then he will take Allison to dinner. This means we can also say that If Ryan does not take Allison to dinner, then he did not get a pay raise is logically equivalent.

**What is logically equivalent examples?**

For example, P→Q is logically equivalent to ⌝P∨Q. So. ⌝(P→Q) is logically equivalent to ⌝(⌝P∨Q).

**Which is logically equivalent to P ∧ Q → R?**

(p ∧ q) → r is logically equivalent to p → (q → r).

### Is the statement p ∧ q ∨ r equivalent to P ∧ Q ∨ R explain?

Since columns corresponding to p∨(q∧r) and (p∨q)∧(p∨r) match, the propositions are logically equivalent.

### Is {[( P ∧ q → R → P → q → R )]} tautology?

Thus, `[(p to q) ^^(q to r) ] to ( p to r)` is a tautolgy. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

**Is P ↔ q equivalent to P ↔ q justify?**

Two propositions p and q are logically equivalent if their truth tables are the same. Namely, p and q are logically equivalent if p ↔ q is a tautology.

**Which of the following propositions is tautology Pvq → Qpv q → P PV P → q Both B & C?**

The correct answer is option (d.) Both (b) & (c). Explanation: (p v q)→q and p v (p→q) propositions is tautology.

## What is the law of identity in logic?

In the formal logic of analytical philosophy, the law of identity is written ” a = a ” or “For all x: x = x “, where a or x refer to a term rather than a proposition, and thus the law of identity is not used in propositional logic. It is that which is expressed by the equals sign “=”, the notion of identity or equality .

## How does the law of identity affect everyday language?

In everyday language, violations of the law of identity introduce ambiguity into the discourse, making it difficult to form an interpretation at the desired level of specificity. The law of identity also allows for substitution.

**What is Leibniz law of identity?**

Gottfried Wilhelm Leibniz claimed that the law of identity (sometimes called “Leibniz’Law”), which he expresses as “Everything is what it is”, is the first primitive truth of reason which is affirmative, and the law of noncontradiction is the first negative truth (Nouv. Ess.

**How to verify that statements are logically equivalent?**

And it will be our job to verify that statements, such as p and q, are logically equivalent. And the easiest way to show equivalence is to create a truth table and see if the columns are identical, as the example below nicely demonstrates