# Logic question: Is ~(P&Q) equivalent to (~P&~Q)?

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

It means that either p is false or q is false or they are both false–anyway, p and q can’t both be true at the same time. So ~(p · q) º ~p v ~q. On the other hand, ~(p v q) means it’s not the case that either p or q. In other words, they ate both not true.

## What is logically equivalent to P?

The last identity says that both (p & p) and (p | p) are logically equivalent to p: If p is true, so are (p & p) and (p | p). If p is false, so are (p & p) and (p | p).

## What is the logical equivalent of P ↔ q?

⌝(P→Q) is logically equivalent to ⌝(⌝P∨Q).

## 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. Some valid argument forms: (1) 1.

## Is ~( Pvq equivalent to P q?

(P VQ) is equivalent to PA-Q. Commutative laws PAQ is equivalent to QAP. PVQ is equivalent to QVP.

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

The negation of p ∧ q asserts “it is not the case that p and q are both true”. Thus, ¬(p ∧ q) is true exactly when one or both of p and q is false, that is, when ¬p ∨ ¬q is true. Similarly, ¬(p ∨ q) can be seen to the same as ¬p ∧ ¬q.

## 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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## Is P ∧ q → P is a tautology?

Since each proposition is logically equivalent to the next, we must have that (p∧q)→(p∨q) and T are logically equivalent. Therefore, regardless of the truth values of p and q, the truth value of (p∧q)→(p∨q) is T. Thus, (p∧q)→(p∨q) is a tautology.

## What is represented by pVq?

Meaning p or q, denoted as pVq, It’s true only when p is true, q is true, or both p and q are true.

## What does pVq mean in truth table?

^ means “and” (conjunction). For example, p ^ q refers to the statement “The art show was enjoyable AND the room was hot”. v means “or” (disjunction) ). For example, p v q refers to the statement “The art show was enjoyable OR the room was hot”. -> means “if then” or “implies”.

## What are the truth values for ~( p ∨ q?

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 T
F T T
F F F

## What is the negation of P q → R?

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

## What is a negation example?

The symbols used to represent the negation of a statement are “~” or “¬”. For example, the given sentence is “Arjun’s dog has a black tail”. Then, the negation of the given statement is “Arjun’s dog does not have a black tail”. Thus, if the given statement is true, then the negation of the given statement is false.

## What does negation mean in logic?

In logic, negation, also called the logical complement, is an operation that takes a proposition to another proposition “not “, written , or . It is interpreted intuitively as being true when is false, and false when is true.

## How do you negate a logical statement?

One thing to keep in mind is that if a statement is true, then its negation is false (and if a statement is false, then its negation is true).
Summary.

Statement Negation
“A or B” “not A and not B”
“A and B” “not A or not B”
“if A, then B” “A and not B”
“For all x, A(x)” “There exist x such that not A(x)”

## What is simple negation give five example?

Negation in Words
Some words such as ever, anybody, anyone, anything, anywhere, instead of never, nobody, no one, nothing, nowhere, etc. represent the Negation. Examples: I do not think he can ever reach within time.

## What is negation statement?

A negation is a refusal or denial of something. If your friend thinks you owe him five dollars and you say that you don’t, your statement is a negation. A negation is a statement that cancels out or denies another statement or action.

## What are 10 examples of negative sentences?

List of Negative Sentences

• I am not flying to England.
• That isn’t the way to Nashville.
• They are not from Ecuador.
• He wasn’t eating white rice.
• We were not sad when he moved away.
• They don’t practice yoga.
• She did not like Bikhram yoga.
• He doesn’t have to commute to work.