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The statement "If not q, then not p" is logically equivalent to "If p, then q."

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5mo ago

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What is the equivalent of an inverse statement?

The equivalent of an inverse statement is formed by negating both the hypothesis and the conclusion of a conditional statement. For example, if the original statement is "If P, then Q" (P → Q), the inverse would be "If not P, then not Q" (¬P → ¬Q). While the inverse is related to the original statement, it is not necessarily logically equivalent.


What are the statements that are always logically equivalent.?

Statements that are always logically equivalent are those that yield the same truth value in every possible scenario. Common examples include a statement and its contrapositive (e.g., "If P, then Q" is equivalent to "If not Q, then not P") and a statement and its double negation (e.g., "P" is equivalent to "not not P"). Additionally, the negation of a statement is logically equivalent to the statement's denial (e.g., "not P" is equivalent to "if not P, then false"). These equivalences play a crucial role in logical reasoning and proofs.


Which statement always has the same truth value as the conditional?

The statement "if not p, then not q" always has the same truth value as the conditional "if p, then q." They are logically equivalent.


What are inverse statement?

An inverse statement is formed by negating both the hypothesis and the conclusion of a conditional statement. For example, if the original conditional statement is "If P, then Q," the inverse is "If not P, then not Q." Inverse statements can help analyze the truth values of the original statement and its contrapositive, but they are not logically equivalent to the original statement.


What is logically equivalent statements?

Logically equivalent statements are expressions or propositions that have the same truth value in every possible scenario. This means that if one statement is true, the other must also be true, and if one is false, the other must be false as well. For example, the statements "If P, then Q" and "If not Q, then not P" (contrapositive) are logically equivalent. Logical equivalence is often denoted using symbols such as "≡" or "⇔".


What does the law of contrapositive state?

The law of contrapositive states that a conditional statement of the form "If P, then Q" (P → Q) is logically equivalent to its contrapositive, "If not Q, then not P" (¬Q → ¬P). This means that if the original statement is true, the contrapositive must also be true, and vice versa. This principle is widely used in mathematical proofs and logical reasoning to demonstrate the validity of arguments.


P-q and q-p are logically equivalent prove?

p --> q and q --> p are not equivalent p --> q and q --> (not)p are equivalent The truth table shows this. pq p --> q q -->(not)p f f t t f t t t t f f f t t t t


How can the statement "p implies q" be expressed in an equivalent form using the logical operator "or" and the negation of "p"?

The statement "p implies q" can be expressed as "not p or q" using the logical operator "or" and the negation of "p".


Is this statement true or false The conditional is the negation of the converse?

The statement is false. The conditional statement "If P, then Q" and its converse "If Q, then P" are distinct statements, but the negation of the converse would be "It is not the case that if Q, then P." Thus, the conditional and the negation of the converse are not equivalent or directly related.


If p q and q r then p r. Converse statement B.A syllogism C.Contrapositive statement D.Inverse statement?

Converse: If p r then p q and q rContrapositive: If not p r then not (p q and q r) = If not p r then not p q or not q r Inverse: If not p q and q r then not p r = If not p q or not q r then not p r


What is logically quivalent to q -- p?

It is: q+p because a double minus becomes a plus


Is the conditional the negation of the Converse?

No, the conditional statement and its converse are not negations of each other. A conditional statement has the form "If P, then Q" (P → Q), while its converse is "If Q, then P" (Q → P). The negation of a conditional statement "If P, then Q" is "P and not Q" (P ∧ ¬Q), which does not relate to the converse directly.