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If a statement's inverse is false, then its converse is false (and vice versa). If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then it is known as a logical biconditional.
Let S be a statement of the form P implies Q (P → Q). Then the converse of S is the statement Q implies P (Q → P). In general, the truth of S says nothing about the truth of its converse, [2] unless the antecedent P and the consequent Q are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal."
The inverse and the converse of a conditional are logically equivalent to each other, just as the conditional and its contrapositive are logically equivalent to each other. [1] But the inverse of a conditional cannot be inferred from the conditional itself (e.g., the conditional might be true while its inverse might be false [2]). For example ...
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
A branch of logic that studies principles of connection between propositions, such as the relation between a statement and its contrapositive. consequence relation A relation between sets of sentences or propositions, where the truth of the first set (the premises) necessitates the truth of the second set (the consequences). consequent
In the early morning hours of Dec. 26, 1996, Patsy Ramsey called 911 to report her 6-year-old daughter JonBenét missing, and found a rambling ransom note left inside their Boulder, Colorado, home.
Given a type A statement, "All S are P.", one can make the immediate inference that "All non-P are non-S" which is the contrapositive of the given statement. Given a type O statement, "Some S are not P.", one can make the immediate inference that "Some non-P are not non-S" which is the contrapositive of the given statement.
Average mortgage rates are edging down moderately week over week of Monday, January 6, 2024, though remain at elevated levels for benchmark 30-year and 15-year fixed terms, this despite three back ...