A Contrapositive statement is logically equivalent.
The conditional statement "If A then B" is equivalent to "Not B or A" So, the inverse of "If A then B" is the inverse of "Not B or A" which is "Not not B and not A", that is "B and not A",
A conditional statement
That is correct.
conditional statement
It is the biconditional.
Contrapositive
a conditional and its contrapositive
This is not always true.
The conditional statement "If A then B" is equivalent to "Not B or A" So, the inverse of "If A then B" is the inverse of "Not B or A" which is "Not not B and not A", that is "B and not A",
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.
An obverse statement is logically equivalent.
The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.
The statement "If not q, then not p" is logically equivalent to "If p, then q."
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.
This would be logically equivalent to the conditional you started with.
A conditional statement uses the words if... Then
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.