Logic question: Is ~(P&Q) 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.

What is logically equivalent to ~( P → Q?

Negation of an Implication.

¬ ( P → Q ) is logically equivalent to P ∧ ¬ Q .

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.

What does Q → P mean?

The converse of a conditional proposition p → q is the proposition q → p. As we have seen, the bi- conditional proposition is equivalent to the conjunction of a conditional proposition an its converse. p ↔ q ≡ (p → q) ∧ (q → p)

What does P stand for in logic?

The logical operation |, also called or and logical disjunction, is an operation on two propositions (a binary operation) that results in another proposition: the proposition (p | q) is true if p is true or if q is true or if both p and q are true.

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What does P mean in logic?

A true-false statement is any sentence that is either true or false but not both. A negation of a statement has the opposite meaning of a truth value. A negations is written as ~p.

How do you show logical equivalence?

To test for logical equivalence of 2 statements, construct a truth table that includes every variable to be evaluated, and then check to see if the resulting truth values of the 2 statements are equivalent.

What is the truth value of the compound proposition P → Q ↔ P if P is false and Q is true?

Tautologies and Contradictions

Operation Notation Summary of truth values
Negation ¬p The opposite truth value of p
Conjunction p∧q True only when both p and q are true
Disjunction p∨q False only when both p and q are false
Conditional p→q False only when p is true and q is false

How do you know if something is logically equivalent?

Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and the second statement can also be true in its own context, they just both have to have the same meaning.

What are the truth values of ~( p Q?

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

How do you write if/p then Q?

Conditional Propositions – A statement that proposes something is true on the condition that something else is true. For example, “If p then q”* , where p is the hypothesis (antecedent) and q is the conclusion (consequent).

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Why are the letters P and Q used in logic?

It is in this that logic plays a role. Basic to deductive thinking is the word “implies,” symbolized by “=>.” A statement p=> q means that whenever p is true, q is true also.
Implication.

p q p=>q
F F T

Under what circumstances is the sentence P → Q true?

The proposition p ↔ q, read “p if and only if q”, is called bicon- ditional. It is true precisely when p and q have the same truth value, i.e., they are both true or both false.

What proposition is true only when exactly one of p and q is true?

The exclusive or of p and q, denoted by pq, is the proposition that is true when exactly one of p and q is true and is false otherwise.

When p is false and q is true then p or q is?

In the truth tables above, there is only one case where “if P, then Q” is false: namely, P is true and Q is false.
IF…., THEN….

P Q If P, then Q
F T T
F F T