## What is Pvq logically equivalent to?

PVQ is equivalent to QVP. Associative laws PA(QAR) is equivalent to (PAQAR. PV(QVR) is equivalent to (PVO) VR.

**What does P ∧ Q mean?**

P ∧ Q means P and Q. P ∨ Q means P or Q. An argument is valid if the following conditional holds: If all the premises are true, the conclusion must be true.

**Is P → Q the same as P → Q?**

Using the same reasoning, or by negating the negation, we can see that p → q is the same as ¬p ∨ q. Finally, the statement p ↔ q asserts that p and q have the same truth value. Hence ¬(p ↔ q) asserts that p and q have different truth values. This happens when p is true and q is false, or when p is false and q is true.

### Is P ∧ Q → R and P → R ∧ Q → R logically equivalent?

Since columns corresponding to ¬(p∨q) and (¬p∧¬q) match, the propositions 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.

**Is P → Q and Pvq are 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.

**How do you read Pvq?**

(p v q) is a proposition, call it r, so read ~(p v q) as “it is not the case that the proposition r is true”. p and q are also propositions, so e.g. ~p is the proposition “it is not the case that p”. Read [(~p) v (~q)] as “it is the case that either (it is not the case that p) or (it is not the case that q).

#### Is Pvq → q tautology?

(p → q) and (q ∨ ¬p) are logically equivalent. So (p → q) ↔ (q ∨ ¬p) is a tautology. Thus: (p → q)≡ (q ∨ ¬p).

**How do you write if/p then q?**

In conditional statements, “If p then q” is denoted symbolically by “p q”; p is called the hypothesis and q is called the conclusion. For instance, consider the two following statements: If Sally passes the exam, then she will get the job. If 144 is divisible by 12, 144 is divisible by 3.

**Which is the inverse of P → q?**

The inverse of p → q is ¬p → ¬q. If p and q are propositions, the biconditional “p if and only if q,” denoted by p ↔ q, is true if both p and q have the same truth values and is false if p and q have opposite truth values.

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

**Is P → Q → R equivalent to P → Q → R?**

Then p→q and q→r are true, so (p→q)→r is false and p→(q→r) is true. Good question!

**What is the meaning of logically equivalent?**

Definition of Logical Equivalence. Formally, Two propositions and are said to be logically equivalent if is a Tautology. The notation is used to denote that and are logically equivalent. One way of proving that two propositions are logically equivalent is to use a truth table.

### How do you prove that two propositions are logically equivalent?

Two propositions and are said to be logically equivalent if is a Tautology. The notation is used to denote that and are logically equivalent. One way of proving that two propositions are logically equivalent is to use a truth table. The truth table must be identical for all combinations for the given propositions to be equivalent.

**What is the best way to construct logical equivalences?**

That better way is to construct a mathematical proof which uses already established logical equivalences to construct additional more useful logical equivalences. The above Logical Equivalences used only conjunction, disjunction and negation. Other logical Equivalences using conditionals and bi-conditionals are-

**Which notation is used to denote that two propositions are logically equivalent?**

The notation is used to denote that and are logically equivalent. One way of proving that two propositions are logically equivalent is to use a truth table. The truth table must be identical for all combinations for the given propositions to be equivalent.