**How to check if two boolean expressions are equivalent**

- Parse the expresion storing it in some structure data.
- Reduce the expresion in OR groups.
- Check if the two expresions have the same groups.

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## How do you know if two expressions are 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.

## What does it mean when two logical expressions are equivalent?

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.

## How can you determine that two propositional expressions are equivalent using a truth table?

To check whether P entails Q, check whether (P ∧ ¬Q) is satisfiable — if so, then P does not entail Q. Similarly check whether (¬P ∧ Q) is satisfiable. If neither is satisfiable, then the formulas are equivalent.

## What is an example of logically equivalent?

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.

## Are P → R ∨ Q → R and P ∧ Q → R logically equivalent?

Since columns corresponding to p∨(q∧r) and (p∨q)∧(p∨r) match, **the propositions are logically equivalent**. This particular equivalence is known as the Distributive Law.

## Which is logically equivalent to P ↔ Q?

P → Q is logically equivalent to **¬ P ∨ Q** . Example: “If a number is a multiple of 4, then it is even” is equivalent to, “a number is not a multiple of 4 or (else) it is even.”

## How do you know if a truth table is logically equivalent?

*So the way we can use truth tables to decide whether. The left side is logically equivalent to the right it's just to make a truth table for each one and see if it works out the same.*

## How do you prove two Boolean expressions are equivalent?

**How to check if two boolean expressions are equivalent**

- Parse the expresion storing it in some structure data.
- Reduce the expresion in OR groups.
- Check if the two expresions have the same groups.

## How do you prove logical equivalence with laws?

*Law to rearrange them and if you remember commutative law P or Q is logically equivalent to Q or P. In. This case we have Q or P. So we can switch them back around to P or Q. – P or Q. And that's I*

## Are P → q and P ∨ q logically equivalent?

**They are logically equivalent**. p ↔ q ≡ (p → q) ∧ (q → p) p ↔ q ≡ ¬p ↔ ¬q p ↔ q ≡ (p ∧ q) ∨ (¬p ∧ ¬q) ¬(p ↔ q) ≡ p ↔ ¬q c Xin He (University at Buffalo) CSE 191 Discrete Structures 28 / 37 Page 14 Prove equivalence By using these laws, we can prove two propositions are logical equivalent.

## What is the negation of ∼ P ∨ q ∧ q ⟶ R )?

Solution. The negation of p ∧ (q → r) is **∼p ∨ (∼q ∧ ∼r)**.

## Which of the proposition is p ∧ P ∨ q is?

The proposition p∧(∼p∨q) is: **a tautology**. **logically equivalent to p∧q**.

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## What is propositional equivalence?

Propositional Equivalences. Def. **A compound proposition that is always true, no matter what the truth values of the (simple) propositions that occur in it**, is called tautology.

## Which of the following pairs of propositions are not logically equivalent?

The above truth table is not equivalent. Hence the above statement is True, Logically not equivalent. ∴ Hence the correct answer is **((p ∧ q) → r ) and ((p → r) ∧ (q → r))**.