# Equivalence of truth conditions?

Contents

## What is the equivalent of a conditional 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 the equivalent truth?

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.

## Are the statements P → Q ∨ R and P → Q ∨ P → are 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.

## How do you know if a truth table is 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.

## What 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 prove logically equivalent?

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.

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

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

## Are these statement are equivalent P ∨ Q and Q ∧ P?

Theorem 2.6. For statements P and Q, The conditional statement P→Q is logically equivalent to ⌝P∨Q. The statement ⌝(P→Q) is logically equivalent to P∧⌝Q.

## What is the truth value of ∼ P ∨ Q ∧ P?

So because we don’t have statements on either side of the “and” symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p.

Truth Tables.

p q p∧q
T F F
F T F
F F F

## Is p ∧ p ∨ Q )) → QA tautology?

All true ∴ Tautology proved.

## Is P ∧ Q → P is 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.

## 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 equivalent to Pvq?

PVQ is equivalent to QVP. Associative laws PA(QAR) is equivalent to (PAQAR.

## Is ~( p q the same as P Q?

~(P&Q) is not the same as (~P&~Q). You can do this for any logic, and it saves a lot of time waiting for answers from StackExchange!